Advertisement

Semigroup Forum

, Volume 89, Issue 1, pp 2–19 | Cite as

John Macintosh Howie: work and legacy

  • Gracinda M. S. GomesEmail author
  • Nik Ruškuc
OBITUARY

References

  1. 1.
    Aĭzenštat, A.J.: The defining relations of the endomorphism semigroup of a finite linearly ordered set (Russian). Sibirsk. Mat. Ž. 3, 161–169 (1962)MathSciNetGoogle Scholar
  2. 2.
    Almeida, J., Moura, A.: Idempotent-generated semigroups and pseudovarieties. Proc. Edinb. Math. Soc. (2) 54, 545–568 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Araújo, I.M.: Finite presentability of semigroup constructions. Int. J. Algebra Comput. 12, 19–31 (2002)CrossRefzbMATHGoogle Scholar
  4. 4.
    Araújo, J.: Idempotent-generated endomorphisms of an independence algebra. Semigroup Forum 67, 464–467 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Araújo, J., Fernandes, V.H., Jesus, M.M., Maltcev, V., Mitchell, J.D.: Automorphisms of partial endomorphism semigroups. Publ. Math. Debr. 79, 23–39 (2011)CrossRefzbMATHGoogle Scholar
  6. 6.
    Ayık, G., Ayık, H., Ünlü, Y., Howie, J.M.: Rank properties of the semigroup of singular transformations on a finite set. Commun. Algebra 36, 2581–2587 (2008)CrossRefzbMATHGoogle Scholar
  7. 7.
    Ballantine, C.S.: Products of idempotent matrices. Linear Algebra Appl. 19, 81–86 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Bergman, G.M.: Generating infinite symmetric groups. Bull. Lond. Math. Soc. 38, 429–440 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Bielas, W., Miller, A.W., Morayne, M., Slonka, T.: Generating Borel measurable mappings with continuous mappings. Topol. Appl. 160, 1439–1443 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Bulman-Fleming, S., Fountain, J., Gould, V.: Inverse semigroups with zero: covers and their structure. J. Aust. Math. Soc. Ser. A 67, 15–30 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Cherubini, A., Howie, J.M., Piochi, B.: Rank and status in semigroup theory. Commun. Algebra 32, 2783–2801 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Cichoń, J., Mitchell, J.D., Morayne, M.: Generating continuous mappings with Lipschitz mappings. Trans. Am. Math. Soc. 359, 2059–2074 (2007)CrossRefzbMATHGoogle Scholar
  13. 13.
    Cichoń, J., Mitchell, J.D., Morayne, M., Péresse, Y.: Relative ranks of Lipschitz mappings on countable discrete metric spaces. Topol. Appl. 158, 412–423 (2011)CrossRefzbMATHGoogle Scholar
  14. 14.
    Dawlings, R.J.H.: Products of idempotents in the semigroup of singular endomorphisms of a finite-dimensional vector space. Proc. R. Soc. Edinb. Sect. A 91, 123–133 (1981/82)Google Scholar
  15. 15.
    Dimitrova, I., Koppitz, J.: On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations. Semigroup Forum 82, 172–180 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Dombi, E.R., Gilbert, N.D.: HNN extensions of inverse semigroups with zero. Math. Proc. Camb. Philos. Soc. 142, 25–39 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    East, J.: Generation of infinite factorizable inverse monoids. Semigroup Forum 84, 267–283 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    East, J., FitzGerald, D.G.: The semigroup generated by the idempotents of a partition monoid. J. Algebra 372, 108–133 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Erdos, J.A.: On products of idempotent matrices. Glasgow Math. J. 8, 118–122 (1967)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Fernandes, V.H.: The monoid of all injective order preserving partial transformations on a finite chain. Semigroup Forum 62, 178–204 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Fernandes, V.H.: Presentations for some monoids of partial transformations on a finite chain: a survey. In: Gomes, G.M.S., Pin, J.-E., Silva, P.V. (eds.) Semigroups, Algorithms, Automata and Languages (Coimbra, 2001), pp. 363–378. World Scientific Publishing, River Edge (2002)Google Scholar
  22. 22.
    Fernandes, V.H., Gomes, G.M.S., Jesus, M.M.: Presentations for some monoids of partial transformations on a finite chain. Commun. Algebra 33, 587–604 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Fleischer, I.: A characterization of selfmaps which are composites of three projections. J. Algebra 238, 459–461 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Fountain, J., Lewin, A.: Products of idempotent endomorphisms of an independence algebra of finite rank. Proc. Edinb. Math. Soc. 35, 493–500 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Fountain, J., Pin, J.-E., Weil, P.: Covers for monoids. J. Algebra 271, 529–586 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Gallagher, P., Ruškuc, N.: On finite generation and presentability of Schützenberger products. J. Aust. Math. Soc. 83, 357–367 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    Galvin, F.: Generating countable sets of permutations. J. Lond. Math. Soc. 51, 230–242 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Ganyushkin, O., Mazorchuk, V.: Combinatorics and distributions of partial injections. Australas. J. Comb. 34, 161–186 (2006)zbMATHMathSciNetGoogle Scholar
  29. 29.
    Gilbert, N.D.: HNN extensions of inverse semigroups and groupoids. J. Algebra 272, 27–45 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Giraldes, E., Howie, J.M.: Embedding finite semigroups in finite semibands of minimal depth. Semigroup Forum 28, 135–142 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  31. 31.
    Giraldes, E., Howie, J.M.: Semigroups of high rank. Proc. Edinb. Math. Soc. (2) 28, 13–34 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  32. 32.
    Gomes, G.M.S., Howie, J.M.: On the ranks of certain finite semigroups of transformations. Math. Proc. Camb. Philos. Soc. 101, 395–403 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  33. 33.
    Gomes, G.M.S., Howie, J.M.: Nilpotents in finite symmetric inverse semigroups. Proc. Edinb. Math. Soc. (2) 30, 383–395 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  34. 34.
    Gomes, G.M.S., Howie, J.M.: On the ranks of certain semigroups of order-preserving transformations. Semigroup Forum 45, 272–282 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  35. 35.
    Gomes, G.M.S., Howie, J.M.: Idempotent endomorphisms of an independence algebra of finite rank. Proc. Edinb. Math. Soc. (2) 38, 107–116 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  36. 36.
    Gomes, G.M.S., Howie, J.M.: A \(P\)-theorem for inverse semigroups with zero. Port. Math. 53, 257–278 (1996)zbMATHMathSciNetGoogle Scholar
  37. 37.
    Gomes, G.M.S., Howie, J.M.: Semigroups with zero whose idempotents form a subsemigroup. Proc. R. Soc. Edinb. Sect. A 128, 265–281 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  38. 38.
    Gould, V.: Independence algebras. Algebra Universalis 33, 294–318 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  39. 39.
    Gray, R., Ruškuc, N.: Generating sets of completely 0-simple semigroups. Commun. Algebra 33, 4657–4678 (2005)CrossRefzbMATHGoogle Scholar
  40. 40.
    Gray, R.: Hall’s condition and idempotent rank of ideals of endomorphism monoids. Proc. Edinb. Math. Soc. (2) 51, 57–72 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  41. 41.
    Gray, R., Pride, S.J.: Homological finiteness properties of monoids, their ideals and maximal subgroups. J. Pure Appl. Algebra 215, 3005–3024 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  42. 42.
    Hawthorn, I., Stokes, T.: Radical decompositions of semiheaps. Comment. Math. Univ. Carol. 50, 191–208 (2009)zbMATHMathSciNetGoogle Scholar
  43. 43.
    Higgins, P.M., Howie, J.M., Ruškuc, N.: Generators and factorisations of transformation semigroups. Proc. R. Soc. Edinb. Sect. A 128, 1355–1369 (1998)CrossRefGoogle Scholar
  44. 44.
    Higgins, P.M., Howie, J.M., Mitchell, J.D., Ruškuc, N.: Countable versus uncountable ranks in infinite semigroups of transformations and relations. Proc. Edinb. Math. Soc. (2) 46, 531–544 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  45. 45.
    Higgins, P.M., Howie, J.M., Ruškuc, N.: Set products in transformation semigroups. Proc. R. Soc. Edinb. Sect. A 133, 1121–1135 (2003)CrossRefzbMATHGoogle Scholar
  46. 46.
    Higgins, P.M., Mitchell, J.D., Morayne, M., Ruškuc, N.: Rank properties of endomorphisms of infinite partially ordered sets. Bull. Lond. Math. Soc. 38, 177–191 (2006)CrossRefzbMATHGoogle Scholar
  47. 47.
    Howie, J.M.: Embedding theorems with amalgamation for semigroups. Proc. Lond. Math. Soc. (3) 12, 511–534 (1962)CrossRefzbMATHMathSciNetGoogle Scholar
  48. 48.
    Howie, J.M.: An embedding theorem with amalgamation for cancellative semigroups. Proc. Glasg. Math. Assoc. 6, 19–26 (1963)CrossRefzbMATHMathSciNetGoogle Scholar
  49. 49.
    Howie, J.M.: Embedding theorems for semigroups. Q. J. Math. Oxf. Ser. (2) 14, 254–258 (1963)CrossRefzbMATHMathSciNetGoogle Scholar
  50. 50.
    Howie, J.M.: The maximum idempotent-separating congruence on an inverse semigroup. Proc. Edinb. Math. Soc. (2) 14, 71–79 (1964/1965)Google Scholar
  51. 51.
    Howie, J.M.: The subsemigroup generated by the idempotents of a full transformation semigroup. J. Lond. Math. Soc. 41, 707–716 (1966)CrossRefzbMATHMathSciNetGoogle Scholar
  52. 52.
    Howie, J.M.: Naturally ordered bands. Glasg. Math. J. 8, 55–58 (1967)CrossRefzbMATHMathSciNetGoogle Scholar
  53. 53.
    Howie, J.M.: Commutative semigroup amalgams. J. Aust. Math. Soc. 8, 609–630 (1968)CrossRefzbMATHMathSciNetGoogle Scholar
  54. 54.
    Howie, J.M.: Products of idempotents in certain semigroups of transformations. Proc. Edinb. Math. Soc. (2) 17, 223–236 (1970/71)Google Scholar
  55. 55.
    Howie, J.M.: Semigroup amalgams whose cores are inverse semigroups. Q. J. Math. Oxf. Ser. (2) 26, 23–45 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  56. 56.
    Howie, J.M.: An Introduction to Semigroup Theory, L.M.S. Monographs, vol. 7. Academic Press, London (1976)Google Scholar
  57. 57.
    Howie, J.M.: Idempotents in completely 0-simple semigroups. Glasg. Math. J. 19, 109–113 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  58. 58.
    Howie, J.M.: Idempotent generators in finite full transformation semigroups. Proc. R. Soc. Edinb. Sect. A 81, 317–323 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  59. 59.
    Howie, J.M.: Products of idempotents in finite full transformation semigroups. Proc. R. Soc. Edinb. Sect. A 86, 243–254 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  60. 60.
    Howie, J.M.: Gravity depth and homogeneity in full transformation semigroups. In: Hall, T.E., Jones, P.R., and Preston, G.B. (eds.) Proceedings of the Monash University Conference on Semigroups, Monash University, Clayton, 1979, pp. 111–119. Academic Press, New York (1980)Google Scholar
  61. 61.
    Howie, J.M.: Some subsemigroups of infinite full transformation semigroups. Proc. R. Soc. Edinb. Sect. A 88, 159–167 (1981)CrossRefzbMATHMathSciNetGoogle Scholar
  62. 62.
    Howie, J.M.: A class of bisimple, idempotent-generated congruence-free semigroups. Proc. R. Soc. Edinb. Sect. A 88, 169–184 (1981)CrossRefzbMATHMathSciNetGoogle Scholar
  63. 63.
    Howie, J.M.: A congruence-free inverse semigroup associated with a pair of infinite cardinals. J. Aust. Math. Soc. Ser. A 31, 337–342 (1981)CrossRefzbMATHMathSciNetGoogle Scholar
  64. 64.
    Howie, J.M.: Products of idempotents in finite full transformation semigroups: some improved bounds. Proc. R. Soc. Edinb. Sect. A 98, 25–35 (1984)CrossRefMathSciNetGoogle Scholar
  65. 65.
    Howie, J.M.: Embedding semigroups in nilpotent-generated semigroups. Math. Slovaca 39, 47–54 (1989)zbMATHMathSciNetGoogle Scholar
  66. 66.
    Howie, J.M.: Automata and Languages. Oxford Science Publications, The Clarendon Press, New York (1991)zbMATHGoogle Scholar
  67. 67.
    Howie, J.M.: Fundamentals of Semigroup Theory, London Mathematical Society Monographs, New Series, vol. 12. Clarendon Press, Oxford (1995)Google Scholar
  68. 68.
    Howie, J.M.: Real Analysis. Springer Undergraduate Mathematics Series. Springer, London (2001)Google Scholar
  69. 69.
    Howie, J.M.: Complex Analysis. Springer Undergraduate Mathematics Series. Springer, London (2003)Google Scholar
  70. 70.
    Howie, J.M.: Fields and Galois Theory. Springer Undergraduate Mathematics Series. Springer, London (2006)Google Scholar
  71. 71.
    Howie, J.M., Lallement, G.: Certain fundamental congruences on a regular semigroup. Proc. Glasg. Math. Assoc. 7, 145–159 (1966)CrossRefzbMATHMathSciNetGoogle Scholar
  72. 72.
    Howie, J.M., Isbell, J.R.: Epimorphisms and dominions II. J. Algebra 6, 7–21 (1967)CrossRefzbMATHMathSciNetGoogle Scholar
  73. 73.
    Howie, J.M., Schein, B.M.: Anti-uniform semilattices. Bull. Aust. Math. Soc. 1, 263–268 (1969)CrossRefzbMATHMathSciNetGoogle Scholar
  74. 74.
    Howie, J.M., Schein, B.M.: Products of idempotent order-preserving transformations. J. Lond. Math. Soc. (2) 7, 357–366 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  75. 75.
    Howie, J.M., Marques-Smith, M.P.: Inverse semigroups generated by nilpotent transformations. Proc. R. Soc. Edinb. Sect. A 99, 153–162 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  76. 76.
    Howie, J.M., Schein, B.M.: Semigroups of forgetful endomorphisms of a finite Boolean algebra. Q. J. Math. Oxf. Ser. (2) 36(143), 283–295 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  77. 77.
    Howie, J.M., Marques-Smith, M.P.: A nilpotent-generated semigroup associated with a semigroup of full transformations. Proc. R. Soc. Edinb. Sect. A 108, 181–187 (1988)CrossRefMathSciNetGoogle Scholar
  78. 78.
    Howie, J.M., Robertson, E.F.: A combinatorial property of finite full transformation semigroups. Proc. R. Soc. Edinb. Sect. A 109, 319–328 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  79. 79.
    Howie, J.M., McFadden, R.B.: Idempotent rank in finite full transformation semigroups. Proc. R. Soc. Edinb. Sect. A 114, 161–167 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  80. 80.
    Howie, J.M., Ruškuc, N.: Constructions and presentations for monoids. Commun. Algebra 22, 6209–6224 (1994)CrossRefzbMATHGoogle Scholar
  81. 81.
    Howie, J.M., Ribeiro, M.I.M.: Rank properties in finite semigroups. Commun. Algebra 27, 5333–5347 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  82. 82.
    Howie, J.M., Ribeiro, M.I.M.: Rank properties in finite semigroups. II. The small rank and the large rank. Southeast Asian Bull. Math. 24, 231–237 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  83. 83.
    Howie, J.M., Lusk, E.L., McFadden, R.B.: Combinatorial results relating to products of idempotents in finite full transformation semigroups. Proc. R. Soc. Edinb. Sect. A 115, 289–299 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  84. 84.
    Howie, J.M., Ruškuc, N., Higgins, P.M.: On relative ranks of full transformation semigroups. Commun. Algebra 26, 733–748 (1998)CrossRefzbMATHGoogle Scholar
  85. 85.
    Isbell, J.R.: Epimorphisms and dominions. In: Proceedings of the Conference on Categorical Algebra (La Jolla, California, 1965), pp. 232–246. Springer, New York (1966)Google Scholar
  86. 86.
    Iwahori, N.: A length formula in a semigroup of mappings. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24, 255–260 (1977)zbMATHMathSciNetGoogle Scholar
  87. 87.
    Kambites, M.: Presentations for semigroups and semigroupoids. Int. J. Algebra Comput. 15, 291–308 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  88. 88.
    Kilp, M., Knauer, U., Mikhalev, A.V.: Monoids, Acts and Categories, de Gruyter Expositions in Mathematics, vol. 29. Walter de Gruyter, Berlin (2000)Google Scholar
  89. 89.
    Kimura, N.: On semigroups. Doctoral thesis, Tulane University (1957)Google Scholar
  90. 90.
    Laradji, A., Umar, A.: On certain finite semigroups of order-decreasing transformations. I. Semigroup Forum 69, 184–200 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  91. 91.
    Laradji, A., Umar, A.: Combinatorial results for the symmetric inverse semigroup. Semigroup Forum 75, 221–236 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  92. 92.
    Lavers, T.G.: Presentations of general products of monoids. J. Algebra 204, 733–741 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  93. 93.
    Levi, I., Mitchell, J.D.: On rank properties of endomorphisms of finite circular orders. Commun. Algebra 34, 1237–1250 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  94. 94.
    Lima, L.M.: Nilpotent local automorphisms of an independence algebra. Proc. R. Soc. Edinb. Sect. A 124, 423–436 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  95. 95.
    Maltcev, V., Mitchell, J.D., Ruškuc, N.: The Bergman property for semigroups. J. Lond. Math. Soc. (2) 80, 212–232 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  96. 96.
    Masat, F.E.: Proper regular semigroups. Proc. Am. Math. Soc. 71, 189–192 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  97. 97.
    Mendes-Gonçalves, S., Sullivan, R.P.: Inverse semigroups generated by linear transformations. Bull. Aust. Math. Soc. 71, 205–213 (2005)CrossRefzbMATHGoogle Scholar
  98. 98.
    Mesyan, Z.: Generating self-map monoids of infinite sets. Semigroup Forum 75, 649–676 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  99. 99.
    Mesyan, Z., Mitchell, J.D., Morayne, M., Péresse, Y.H.: The Bergman-Shelah preorder on transformation semigroups. Math. Log. Q. 58, 424–433 (2012)CrossRefzbMATHGoogle Scholar
  100. 100.
    Mitchell, J.D., Péresse, Y., Quick, M.R.: Generating sequences of functions. Q. J. Math. 58, 71–79 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  101. 101.
    Péresse, Y.: Generating uncountable transformation semigroups. Ph.D. Thesis, St Andrews (2009)Google Scholar
  102. 102.
    Preston, G.B.: A characterization of inaccessible cardinals. Proc. Glasg. Math. Assoc. 5, 153–157 (1962)CrossRefzbMATHMathSciNetGoogle Scholar
  103. 103.
    Renshaw, J.: Extension and amalgamation in monoids, semigroups and rings. Ph.D. Thesis, University of St Andrews (1985)Google Scholar
  104. 104.
    Renshaw, J.: Extension and amalgamation in rings. Proc. R. Soc. Edinb. Sect. A 102, 103–115 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  105. 105.
    Renshaw, J.: Flatness and amalgamation in monoids. J. Lond. Math. Soc. (2) 33, 73–88 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  106. 106.
    Renshaw, J.: Extension and amalgamation in monoids and semigroups. Proc. Lond. Math. Soc. (3) 52, 119–141 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  107. 107.
    Ruškuc, N.: On the rank of completely 0-simple semigroups. Math. Proc. Camb. Philos. Soc. 116, 325–338 (1994)CrossRefzbMATHGoogle Scholar
  108. 108.
    Sierpiśki, W.: Sur les suites infinies de fonctions définies dans les ensembles quelconques. Fundam. Math. 24, 209–212 (1935)Google Scholar
  109. 109.
    Sullivan, R.P.: Products of nilpotent matrices. Linear Multilinear Algebra 56, 311–317 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  110. 110.
    Tabatabaie Shourijeh, B., Jokar, A.: Tight representations of 0-\(E\)-unitary inverse semigroups, Abstr. Appl. Anal. Art. ID 353584, 6 (2011)Google Scholar
  111. 111.
    Wang, L.-M., Feng, Y.-Y.: \(E\omega \)-Clifford congruences and \(E\omega \text{- }E\)-reflexive congruences on an inverse semigroup. Semigroup Forum 82, 354–366 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  112. 112.
    Yamamura, A.: HNN extensions of inverse semigroups and applications. Int. J. Algebra Comput. 7, 605–624 (1997)CrossRefMathSciNetGoogle Scholar
  113. 113.
    Yamamura, A.: HNN extensions of semilattices. Int. J. Algebra Comput. 9, 555–596 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  114. 114.
    Yamamura, A.: Embedding theorems for HNN extensions of inverse semigroups. J. Pure Appl. Algebra 210, 521–536 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  115. 115.
    Zhao, P., Xu, B., Yang, M.: A note on maximal properties of some subsemigroups of finite order-preserving transformation semigroups. Commun. Algebra 40, 1116–1121 (2012)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Departamento de Matemática and Centro de Álgebra (CAUL), Faculdade de CiênciasUniversidade de LisboaLisbon Portugal
  2. 2.School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsScotland, UK

Personalised recommendations