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2015 | 13 | 1 |
Tytuł artykułu

On Vn-semigroups

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we give some new characterizations of orthodox semigroups in terms of the set of inverses of idempotents. As a generalization, a new class of regular semigroups, namely Vn-semigroups, is introduced. Also, we give a characterization of Vn-semigroups and investigate some properties of Vn-semigroups. Furthermore, we show that the class of Vn-semigroups is closed under direct products and homomorphic images. However, regular subsemigroups of Vn-semigroups (n ≥ 2) are not necessarily Vn-semigroups in general. Therefore, the class of Vn-semigroups (n ≥ 2) does not form an e-variety. Finally, we obtain that a E-solid semigroup S is a V2-semigroup if and only if S is orthodox.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-11-18
zaakceptowano
2015-12-03
online
2015-12-18
Twórcy
autor
  • Department of Mathematics, South China University of Technology, Guangzhou, Guangdong, 510640, P.R. China
autor
  • Department of Mathematics, South China University of Technology, Guangzhou, Guangdong, 510640, P.R. China
Bibliografia
  • [1] Howie, J.M., Fundamentals of Semigroup Theory, Oxford University Press, New York, 1995
  • [2] Hall, T.E., On regular semigroups, Journal of Algebra, 1973, 24(1), 1-24[Crossref]
  • [3] Hall, T.E., On regular semigroups whose idempotents form a subsemigroup, Bulletin of the Australian Mathematical Society, 1969,1(02), 195-208[WoS]
  • [4] Petrich, M., Inverse semigroups, Wiley, New York, 1984
  • [5] Petrich, M., Reilly, N.R., Completely regular semigroups, Wiley, New York, 1999
  • [6] Yamada, M., Structure of quasi-orthodox semigroups, Memoirs of the Faculty of Science Shimane University, 1980, 14, 1-18
  • [7] Blyth, T.S., McFadden, R.B., Regular semigroups with a multiplicative inverse transversal, Proceedings of the Royal Society ofEdinburgh: Section A Mathematics, 1982, 92, 253-270
  • [8] Tang, X.L., Regular semigroups with inverse transversals, Semigroup Forum, 1997, 55(1), 24-32[WoS][Crossref]
  • [9] Guo, X.J., Shum, K.P., Abundant semigroups with Q-adequate transversals and some of their special cases, Algebra Colloquium,2007, 14, 687-704[WoS][Crossref]
  • [10] Tang, X.L., Identities for a class of regular unary semigroups, Communications in Algebra, 2008, 36, 2487-2502[Crossref][WoS]
  • [11] Tang, X.L., Free orthodox semigroups and free bands with inverse transversals, Science China Mathematics, 2010, 53(11), 3015-3026[WoS]
  • [12] Tang, X.L., Gu, Z., Words on free bands with inverse transversals, Semigroup Forum, 2015, 91, 101-116[WoS]
  • [13] Wang, L.M., On congruence lattices of regular semigroups with Q-inverse transversals, Semigroup Forum, 1995, 50, 141-160[Crossref]
  • [14] Fitz-Gerald, D.G., On inverses of products of idempotents in regular semigroups, Journal of the Australian Mathematical Society,1972, 13, 335-337[Crossref]
  • [15] Hall, T.E., Congruences and Green’s relations on regular semigroups, Glasgow Mathematical Journal, 1972, 13(02), 167-175[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0085
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