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A system of bi-identities for locally inverse semigroups


Author: K. Auinger
Journal: Proc. Amer. Math. Soc. 123 (1995), 979-988
MSC: Primary 20M18
DOI: https://doi.org/10.1090/S0002-9939-1995-1291762-0
MathSciNet review: 1291762
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Abstract: A class of regular semigroups closed under taking direct products, regular subsemigroups, and homomorphic images is an existence-variety (or e-variety) of regular semigroups. Each e-variety of locally inverse semigroups can be characterized by a set of bi-identities. These are identities of terms of type $ \langle 2,2\rangle $ in two sorts of variables X and $ X'$. In this paper we obtain a basis of bi-identities for the e-variety of locally inverse semigroups and for certain sub-e-varieties.


References [Enhancements On Off] (What's this?)

  • [1] K. Auinger, The bifree locally inverse semigroup on a set, J. Algebra 166 (1994), 630-650. MR 1280594 (95h:20081)
  • [2] -, The word problem for the bifree combinatorial strict regular semigroup, Math. Proc. Cambridge Philos. Soc. 113 (1993), 519-533. MR 1207517 (94b:20061)
  • [3] A. H. Clifford, The free completely regular semigroup on a set, J. Algebra 59 (1979), 434-451. MR 543262 (80h:20082a)
  • [4] G. Grätzer, Universal algebra, Van Nostrand, New York, 1968. MR 0248066 (40:1320)
  • [5] T. E. Hall, Congruences and Green's relations on regular semigroups, Glasgow Math. J. 13 (1972), 167-175. MR 0318356 (47:6903)
  • [6] -, Identities for existence varieties of regular semigroups, Bull. Austral. Math. Soc. 40 (1989), 59-77. MR 1020841 (90j:20127)
  • [7] -, Regular semigroups: amalgamation and the lattice of existence varieties, Algebra Universalis 29 (1991), 79-108. MR 1083823 (92g:20098)
  • [8] -, A concept of variety for regular semigroups, Semigroup Theory, Proceedings of the Monash University Conference on Semigroup Theory in Honor of G. P. Preston (T. E. Hall, P. R. Jones, and J. C. Meakin, eds.), World Scientific, Singapore, 1991, pp. 101-116. MR 1232677 (94g:20083)
  • [9] J. M. Howie, An introduction to semigroup theory, Academic Press, London, 1976. MR 0466355 (57:6235)
  • [10] J. Kaďourek and M. B. Szendrei, A new approach in the theory of orthodox semigroups, Semigroup Forum 40 (1990), 257-296. MR 1038007 (91k:20075)
  • [11] J. C. Meakin, Local semilattices on two generators, Semigroup Forum 24 (1982), 95-116. MR 650566 (83g:20068)
  • [12] -, The free local semilattice on a set, J. Pure Appl. Algebra 27 (1983), 263-275. MR 688758 (84e:20070)
  • [13] J. C. Meakin and F. Pastijn, The structure of pseudosemilattices, Algebra Universalis 13 (1981), 355-372. MR 631728 (82k:20100)
  • [14] -, The free pseudosemilattice on two generators, Algebra Universalis 14 (1982), 297-309. MR 654399 (83f:06005)
  • [15] K. S. S. Nambooripad, Structure of regular semigroups, Mem. Amer. Math. Soc., vol. 224, Amer. Math. Soc., Providence, RI, 1979. MR 546362 (81i:20086)
  • [16] -, The natural partial order on a regular semigroup, Proc. Edinburgh Math. Soc. (2) 23 (1980), 249-260. MR 620922 (82g:20092)
  • [17] -, Pseudosemilattices and biordered sets I, Simon Stevin 55 (1981), 103-110. MR 635096 (83d:06003)
  • [18] -, Pseudosemilattices and biordered sets II, Simon Stevin 56 (1982), 143-160. MR 669189 (84f:20071a)
  • [19] -, Pseudosemilattices and biordered sets III, Simon Stevin 56 (1982), 239-256. MR 687502 (84f:20071b)
  • [20] F. Pastijn, Rectangular bands of inverse semigroups, Simon Stevin 56 (1982), 1-97. MR 662981 (83i:20063)
  • [21] -, The structure of pseudo-inverse semigroups, Trans. Amer. Math. Soc. 273 (1982), 631-655. MR 667165 (84c:20072)
  • [22] M. Petrich, Inverse semigroups, Wiley, New York, 1984. MR 752899 (85k:20001)
  • [23] B. M. Schein, Pseudosemilattices and pseudolattices, Izv. Vyssh. Uchebn. Zaved. Mat. 117 (1972), 81-94; English transl.Amer. Math. Soc. Transl. 119 (1983), 1-16.
  • [24] M. B. Szendrei, Free $ \ast $-orthodox semigroups, Simon Stevin 59 (1985), 175-201. MR 805105 (86k:20054)
  • [25] P. G. Trotter, Normal partitions of idempotents of regular semigroups, J. Austral. Math. Soc. 26 (1978), 110-114. MR 510594 (80c:20088)
  • [26] Y. T. Yeh, The existence of e-free objects in e-varieties of regular semigroups, Internat. J. Algebra Comput. 2 (1992), 471-484. MR 1189674 (94d:20085)

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DOI: https://doi.org/10.1090/S0002-9939-1995-1291762-0
Article copyright: © Copyright 1995 American Mathematical Society

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