Skip to main content
SpringerLink
Log in

Extensions of seminearrings by semigroups of right quotients

  • Conference paper
  • First Online:
Book cover Recent Developments in the Algebraic, Analytical, and Topological Theory of Semigroups

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 998))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Botero de Meza, M.M., Zur Theorie allgemeiner Rechtsquotientenhalbgruppen und Rechtsquotientenhalbringe, Dissertation, Technische Universität Clausthal (1975).

    Google Scholar 

  2. Bourbaki, N., Eléments de Mathématique, 27, Algèbre Commutative, Chap. I, II, Paris (1961).

    Google Scholar 

  3. Bourne, S., The Jacobson radical of a semiring, Proc. Nat. Acad. Sci. USA 37 (1951), 163–170.

    Article  MathSciNet  MATH  Google Scholar 

  4. Bourne, S. and H. Zassenhaus, On the semiradical of a semiring, Proc. Nat. Acad. Sci. USA 44 (1958), 907–914.

    Article  MathSciNet  MATH  Google Scholar 

  5. Chew, K.L. and G.H. Chan, On extensions of near-rings, Nanta Math. 5 (1971), 12–21.

    MathSciNet  MATH  Google Scholar 

  6. Clifford, A.H. and G.B. Preston, The algebraic theory of semigroups, Amer. Math. Soc. Vol.I (1961), Vol.II (1967).

    Google Scholar 

  7. Faith, C., Lectures on injective modules and quotient rings, Lecture Notes in Mathematics 49 (1967).

    Google Scholar 

  8. Fuchs, L., Teilweise geordnete algebraische Strukturen, Vandenhoeck & Ruprecht (1966).

    Google Scholar 

  9. Grillet, M.P., Embedding of a semiring into a semiring with identity, Acta Math. Acad. Sci. Hungar. 20 (1969), 121–128.

    Article  MathSciNet  MATH  Google Scholar 

  10. Hebisch, U., On right quotient filters of semigroups, this Lecture Notes.

    Google Scholar 

  11. Hinkle, C.V., Jr., Semigroups of right quotients of a semigroup which is a semilattice of groups, Semigroup Forum 5 (1972), 167–173.

    Article  MathSciNet  MATH  Google Scholar 

  12. Hogewijs, H., Semi-nearrings-embedding, Med. Konink. Acad. Wetensch. Lett. Schone Kunst, België Kl. Wetensch. 32 (1970), 3–11.

    Google Scholar 

  13. van Hoorn, W.G., Some generalizations of the Jacobson radical for seminearrings and semirings, Math. Z. 118 (1970), 69–82.

    Article  MathSciNet  MATH  Google Scholar 

  14. van Hoorn, W.G. and G. van Rootselaar, Fundamental notions in the theory of seminearrings, Comp. Math. 18 (1967), 65–78.

    MathSciNet  MATH  Google Scholar 

  15. Huq, S.A., The semiring of quotients of commutative semirings, Colloq. Math. 28 (1973), 185–188.

    MathSciNet  MATH  Google Scholar 

  16. Iizuka, K., On the Jacobson radical of a semiring, Tohoku Math. J. 2 (1959), 409–421.

    Article  MathSciNet  MATH  Google Scholar 

  17. Iséki, K. and Y. Miyanaga, Notes on topological spaces III. On space of maximal ideals of semiring, Proc. Japan Acad. 32 (1956), 325–328.

    Article  MathSciNet  MATH  Google Scholar 

  18. Johnson, R.E., The extended centralizer of a ring over a modul, Proc. Amer. Math. Soc. 2 (1951), 891–895.

    Article  MathSciNet  MATH  Google Scholar 

  19. Karzel, H., Zusammenhänge zwischen Fastbereichen, scharf zweifach transitiven Permutationsgruppen und 2-Strukturen mit Rechtecksaxiom, Abh. Math. Sem. Univ. Hamburg 32 (1969), 191–206.

    Article  MathSciNet  MATH  Google Scholar 

  20. Kerby, W. and H. Wefelscheid, Bemerkungen über Fastbereiche und scharf zweifach transitive Gruppen, Abh. Math. Sem. Univ. Hamburg 37 (1972), 20–29.

    Article  MathSciNet  MATH  Google Scholar 

  21. LaTorre, D.R., On h-ideals and k-ideals in hemirings, Publ. Math. Debrecen 12 (1965), 219–226.

    MathSciNet  Google Scholar 

  22. Luedeman, J.K., A generalization of the concept of a ring of quotients, Canad. Math. Bull. 14 (1971) 517–529.

    Article  MathSciNet  MATH  Google Scholar 

  23. Luedeman, J.K., Torsion theories and semigroups of quotients, this Lecture Notes.

    Google Scholar 

  24. McMorris, F.R., The maximal quotient semigroup, Semigroup Forum 4 (1972), 360–364.

    Article  MathSciNet  MATH  Google Scholar 

  25. Pilz, G., Geordnete Fastringe, Abh. Math. Sem. Univ. Hamburg 35 (1970), 83–88.

    Article  MathSciNet  MATH  Google Scholar 

  26. Pilz, G., Near-Rings, North-Holland Publ. Comp. (1977).

    Google Scholar 

  27. Rédei, L., Die Verallgemeinerung der Schreierschen Erweiterungstheorie, Acta Sci. Math. (Szeged) 14 (1952), 252–273.

    MathSciNet  MATH  Google Scholar 

  28. Rédei, L., Algebra, Budapest (1954), Leipzig (1959), London (1967).

    Google Scholar 

  29. van Rootselaar, B., Algebraische Kennzeichnung freier Wortarithmetiken, Comp. Math. 15 (1963), 156–186.

    MathSciNet  MATH  Google Scholar 

  30. Steinfeld, O., Über die Struktursätze der Semiringe, Acta Math. Acad. Sci. Hungar. 10 (1959), 149–155.

    Article  MathSciNet  MATH  Google Scholar 

  31. Utumi, Y., On quotient rings, Osaka Math. J. 8 (1956), 1–18.

    MathSciNet  MATH  Google Scholar 

  32. Vandiver, H.S., Note on a simple type of algebra in which the cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40 (1934), 914–920.

    Article  MathSciNet  MATH  Google Scholar 

  33. Wefelscheid, H., ZT-subgroups of sharply 3-transitive groups, Proc. Edinburgh Math. Soc. (2) 23 (1980), 9–14.

    Article  MathSciNet  MATH  Google Scholar 

  34. Weinert, H.J., Über Halbringe und Halbkörper II, Acta Math. Acad. Sci. Hungar. 14 (1963), 209–227.

    Article  MathSciNet  MATH  Google Scholar 

  35. Weinert, H.J., Ringe mit nichtkommutative Addition I, Jber. Deutsch. Math.-Verein. 77 (1975), 10–27.

    MathSciNet  MATH  Google Scholar 

  36. Weinert, H.J., Zur Erweiterung algebraischer Strukturen durch Rechtsquotientenbildung, Acta Math. Acad. Sci. Hungar. 16 (1965), 213–214.

    Article  MathSciNet  MATH  Google Scholar 

  37. Weinert, H.J., On the extension of partial orders on semigroups of right quotients, Trans. Amer. Math. Soc. 142 (1969), 345–353.

    MathSciNet  MATH  Google Scholar 

  38. Weinert, H.J., Related representation theorems for rings, semirings, near-rings and semi-near-rings by partial transformations and partial endomorphisms, Proc. Edinburgh Math. Soc. 20 (1976–77), 307–315.

    Article  MathSciNet  MATH  Google Scholar 

  39. Weinert, H.J., S-sets and semigroups of quotients, Semigroup Forum 19 (1980), 1–78.

    Article  MathSciNet  MATH  Google Scholar 

  40. Weinert, H.J., Seminearrings, seminearfields and their semigroup-theoretical background, Semigroup Forum 24 (1982), 231–254.

    Article  MathSciNet  MATH  Google Scholar 

  41. Weinert, H.J., Zur Theorie der Halbfastkörper, to appear in Studia Sci. Math. Hungar.

    Google Scholar 

  42. Weinert, H.J. and R.D. Griepentrog, Embedding semirings by translational hulls, Semigroup Forum 14 (1977), 235–246.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Clausthal, Erzstraße 1, D-3392, Clausthal-Zellerfeld

    Hanns Joachim Weinert

Authors
  1. Hanns Joachim Weinert
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Karl Heinrich Hofmann Helmut Jürgensen Hanns Joachim Weinert

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Weinert, H.J. (1983). Extensions of seminearrings by semigroups of right quotients. In: Hofmann, K.H., Jürgensen, H., Weinert, H.J. (eds) Recent Developments in the Algebraic, Analytical, and Topological Theory of Semigroups. Lecture Notes in Mathematics, vol 998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062045

Download citation

  • DOI: https://doi.org/10.1007/BFb0062045

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12321-7

  • Online ISBN: 978-3-540-40051-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation