Axioms for unary semigroups via division operations

Araújo, João; Kinyon, Michael

http://hdl.handle.net/10400.2/3796

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Authors

Araújo, João

Kinyon, Michael

Abstract(s)

When a semigroup has a unary operation, it is possible to define two bin ary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to extend those results to other classes of unary semigroups. In the first part of the paper we provide characterizations for several classes of unary semigroups, including (a special class of) E-inversive, regular, completely regular, inverse, Clifford, etc., in terms of left and right division. In the second part we solve a problem that was posed elsewhere. The paper closes with a list of open problems.

Keywords

Bigroupoid Clifford semigroups Completely regular E-inversive semigroups Inverse semigroups

URI

http://hdl.handle.net/10400.2/3796

Citation

Araújo, João; Kinyon, Michael - Axioms for unary semigroups via division operations. "Communications in Algebra" [Em linha]. ISSN 0092-7872 (Print) 1532-4125 (Online). Vol. 40, nº 2 (2012), p. 1-17