PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2011 | 9 | 1 | 1-22
Tytuł artykułu

Finite basis problem for 2-testable monoids

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A monoid S 1 obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S 1 is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
1
Strony
1-22
Opis fizyczny
Daty
wydano
2011-02-01
online
2010-12-30
Twórcy
autor
Bibliografia
  • [1] Almeida J., Finite Semigroups and Universal Algebra, Series in Algebra, 3, World Scientific, Singapore, 1994
  • [2] Burris S., Sankappanavar H.P., A Course in Universal Algebra, Grad. Texts in Math., 78, Springer, New York-Heidelberg-Berlin, 1981
  • [3] Edmunds C.C., On certain finitely based varieties of semigroups, Semigroup Forum, 1977, 15(1), 21–39 http://dx.doi.org/10.1007/BF02195732
  • [4] Edmunds C.C., Varieties generated by semigroups of order four, Semigroup Forum, 1980, 21(1), 67–81 http://dx.doi.org/10.1007/BF02572537
  • [5] Hall T.E., Kublanovskii S.I., Margolis S., Sapir M.V., Trotter P.G., Algorithmic problems for finite groups and finite 0-simple semigroups, J. Pure Appl. Algebra, 1997, 119(1), 75–96 http://dx.doi.org/10.1016/S0022-4049(96)00050-3
  • [6] Lee E.W.H., Identity bases for some non-exact varieties, Semigroup Forum, 2004, 68(3), 445–457 http://dx.doi.org/10.1007/s00233-003-0029-5
  • [7] Lee E.W.H., Subvarieties of the variety generated by the five-element Brandt semigroup, Internat. J. Algebra Comput., 2006, 16(2), 417–441 http://dx.doi.org/10.1142/S0218196706002998
  • [8] Lee E.W.H., On identity bases of exclusion varieties for monoids, Comm. Algebra, 2007, 35(7), 2275–2280 http://dx.doi.org/10.1080/00927870701328722
  • [9] Lee E.W.H., Combinatorial Rees-Sushkevich varieties are finitely based, Internat. J. Algebra Comput., 2008, 18(5), 957–978 http://dx.doi.org/10.1142/S0218196708004755
  • [10] Lee E.W.H., On the variety generated by some monoid of order five, Acta Sci. Math. (Szeged), 2008, 74(3–4), 509–537
  • [11] Lee E.W.H., Hereditarily finitely based monoids of extensive transformations, Algebra Universalis, 2009, 61(1), 31–58 http://dx.doi.org/10.1007/s00012-009-0001-7
  • [12] Lee E.W.H., Combinatorial Rees-Sushkevich varieties that are Cross, finitely generated, or small, Bull. Aust. Math. Soc., 2010, 81(1), 64–84 http://dx.doi.org/10.1017/S0004972709000616
  • [13] Lee E.W.H., Varieties generated by 2-testable monoids (submitted)
  • [14] Lee E.W.H., Li J.R., Minimal non-finitely based monoids (submitted)
  • [15] Lee E.W.H., Volkov M.V., On the structure of the lattice of combinatorial Rees-Sushkevich varieties, In: Semigroups and Formal Languages, Lisboa, 2005, World Scientific, Singapore, 2007, 164–187
  • [16] Lee E.W.H., Volkov M.V., Limit varieties generated by completely 0-simple semigroups, Internat. J. Algebra Comput. (in press)
  • [17] Luo Y.F., Zhang W.T., On the variety generated by all semigroups of order three (submitted)
  • [18] Perkins P., Bases for equational theories of semigroups, J. Algebra, 1969, 11(2), 298–314 http://dx.doi.org/10.1016/0021-8693(69)90058-1
  • [19] Sapir M.V., Problems of Burnside type and the finite basis property in varieties of semigroups, Math. USSR, Izv., 1988, 30(2), 295–314 http://dx.doi.org/10.1070/IM1988v030n02ABEH001012
  • [20] Shevrin L.N., Volkov M.V., Identities of semigroups, Soviet Math. (Iz. VUZ), 1985, 29(11), 1–64
  • [21] Torlopova N.G., Varieties of quasi-orthodox semigroups, Acta Sci. Math. (Szeged), 1984, 47(3–4), 297–301 (in Russian)
  • [22] Trahtman A.N., The finite basis question for semigroups of order less than six, Semigroup Forum, 1983, 27(1), 387–389 http://dx.doi.org/10.1007/BF02572749
  • [23] Trahtman A.N., Some finite infinitely basable semigroups, Ural. Gos. Univ. Mat. Zap., 1987, 14(2), 128–131 (in Russian)
  • [24] Trahtman A.N., Identities of a five-element 0-simple semigroup, Semigroup Forum, 1994, 48(3), 385–387 http://dx.doi.org/10.1007/BF02573687
  • [25] Trahtman A.N., Identities of locally testable semigroups, Comm. Algebra, 1999, 27(11), 5405–5412 http://dx.doi.org/10.1080/00927879908826762
  • [26] Volkov M.V., The finite basis question for varieties of semigroups, Math. Notes, 1989, 45(3), 187–194
  • [27] Volkov M.V., The finite basis problem for finite semigroups, Sci. Math. Jpn., 2001, 53(1), 171–199
  • [28] Zhang W.T., Some Studies on Varieties Generated by Finite Semigroups and Their Subvarieties Lattices, PhD thesis, Lanzhou University, Gansu, China, 2009 (in Chinese)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0080-x
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.