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TitleF-regular semigroups
Author(s)Smith, M. Paula Marques
Giraldes, E.
Mitsch, H.
Regular semigroup
Natural partial order
Issue date2004
JournalJournal of Algebra
Citation"Journal of Algebra". ISSN 0021- 8693. 247:2 (2004) 491-510.
Abstract(s)A semigroup S is called F-regular if S is regular and if there exists a group congruence rho on S such that every rho-class contains a greatest element with respect to the natural partial order of S (see [K.S. Nambooripad, Proc. Edinburgh Math. Soc. 23 (1980) 249-260]). These semigroups were investigated in [C.C. Edwards, Semigroup Forum 19 (1980) 331-345] where a description similar to the F-inverse case (see [R. McFadden, L. O'Carroll, Proc. London Math. Soc. 22 (1971) 652-666]) is given. Further characterizations of F-regular semigroups, including an axiomatic one, are provided. The main objective is to give a new representation of such semigroups by means of Szendrei triples (see [M. Szendrei, Acta Sci. Math. 51 (1987) 229-249]). The particular case of F-regular semigroups S satisfying the identity (xy)* = y*x*, where x* epsilon S denotes the greatest element of the rho-class containing x epsilon S, is considered. Also the F-inversive semigroups, for which this identity holds, are characterized. (C) 2004 Elsevier Inc. All rights reserved.
ISSN0021- 8693
Publisher version ArticleURL&_udi=B6WH2-4BP3JHP-1&_user= 10&_coverDate=04%2F15%2F2004&_alid= 664478190&_rdoc=1&_fmt=summary&_orig= search&_cdi=6838&_sort=d&_docanchor= &view=c&_ct=1&_acct=C000050221&_version= 1&_urlVersion=0&_userid=10&md5= b96ebda0467adad139ba92827e53789a
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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