Skip to main content
Log in

Bases of identities of varieties of inverse semigroups

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. A. Yu. Ol'shanskii, “On the problem of a finite basis of identities in groups,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 2, 376–387 (1970).

    Google Scholar 

  2. S. I. Adyan, “Infinite irreducible sets of group identities,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 4, 715–734 (1970).

    Google Scholar 

  3. M. R. Lee-Vaughan, “Uncountably many varieties of groups,” Bull. London Math. Soc.,2, No. 6, 280–286 (1970).

    Google Scholar 

  4. A. P. Biryukov, “On infinite sets of identities in semigroups,” Algebra Logika,4, No. 2, 31–32 (1965).

    Google Scholar 

  5. K. A. Baker, “Equational classes of modular lattices,” Pac. J. Math.,28, No. 1, 9–15 (1969).

    Google Scholar 

  6. P. Perkins, “Bases for equational theories of semigroups,” J. Algebra,11, No. 2, 298–314 (1969).

    Google Scholar 

  7. S. V. Polin, “On identities of finite algebras,” Sib. Mat. Zh.,17, No. 6, 1356–1366 (1976).

    Google Scholar 

  8. S. Oates and M. B. Powell, “Identical relations in finite groups,” J. Algebra,1, No. 1, 11–39 (1964).

    Google Scholar 

  9. I. V. L'vov, “On varieties of associate rings. I,” Algebra Logika,12, No. 3, 269–297 (1973).

    Google Scholar 

  10. R. L. Kruze, “Identities satisfied by a finite ring,” J. Algebra,26, No. 2, 298–318 (1973).

    Google Scholar 

  11. R. McKenzie, “Equational bases for lattice theories,” Math. Scand.,27, No. 1, 24–38 (1970).

    Google Scholar 

  12. A. H. Clifford and G. B. Preston, Algebraic Theory of Semigroups, Vols 1, 2, Amer. Math. Soc. (1967).

  13. B. M. Shain, “On the theory of generalized groups and generalized heaps,” in: Theory of Semigroups and Its Applications [in Russian], No. 1, Saratov Univ. (1965), pp. 286–324.

  14. E. I. Kleiman, “On the structure of varieties of inverse semigroups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 106–109 (1976).

    Google Scholar 

  15. E. I. Kleiman, “On basis of identities of Brandt semigroups,” Semigroup Forum,13, No. 3, 209–218 (1977).

    Google Scholar 

  16. A. I. Mal'tsev, “On multiplication of classes of algebraic systems,” Sib. Mat. Zh.,8, No. 2, 346–365 (1967).

    Google Scholar 

  17. R. J. Warne, “Extensions of Brandt semigroups and applications,” Illinois J. Math.,10, No. 4, 652–660 (1966).

    Google Scholar 

  18. M. Petrich, “Produit, cartésien de demi-groupes completement simples,” C. R. Acad. Sci.,259, No. 2, 277–279 (1964).

    Google Scholar 

  19. E. I. Kleiman, “On free inverse semigroups,” Mat. Zap. Ural. Univ.,8, No. 3, 49–72 (1972).

    Google Scholar 

  20. A. I. Mal'tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  21. L. M. Gluskin, “Elementary generalized groups,” Mat. Sb.,41, No. 1, 23–36 (1957).

    Google Scholar 

  22. T. I. Ershova, “On monogenically inverse semigroups,” Mat. Zap. Ural. Univ.,8, No. 1, 30–33 (1971).

    Google Scholar 

  23. G. G. Dyachenko and B. M. Shain, “The structure of finite monogenic inverse semigroups,” Mat. Zap. Ural. Univ.,9, No. 1, 15–21 (1974).

    Google Scholar 

  24. G. G. Dyachenko and B. M. Shain, “Monogenic inverse semigroups,” in: Algebra and Number Theory [in Russian], No. 1, Kabardino-Balkarsk. Univ., Nal'chik (1973), pp. 3–26.

    Google Scholar 

  25. Kourovskii Notebook [in Russian], Inst. Mat. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1973).

  26. M. F. Newman, “Just non-finitely-based varieties of groups,” Bull. Austral. Math. Soc.,4, No. 3, 343–348 (1971).

    Google Scholar 

  27. D. B. McAlister, “Groups, semilattices, and inverse semigroups. II,” Trans. Am. Math. Soc.,196, 354–370 (1974).

    Google Scholar 

  28. M. R. Lee-Vaughan, “On product varieties of groups,” Bull. Austral. Math. Soc.5, No. 2, 239–240 (1971).

    Google Scholar 

  29. Yu. G. Kleiman, “On a basis for a product of varieties of groups. II,” Izv. Akad. Nauk SSSR, Ser. Mat.38, No. 3, 475–483 (1974).

    Google Scholar 

Download references

Authors

Additional information

State Pedagogic University, Sverdlovsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 20, No. 4, pp. 760–777, July–August, 1979.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kleiman, E.I. Bases of identities of varieties of inverse semigroups. Sib Math J 20, 530–543 (1979). https://doi.org/10.1007/BF00970367

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00970367

Keywords

Navigation