Vol. 90, No. 2, 1980

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ISSN: 0030-8730
On bisimple weakly inverse semigroups

S. Madhavan

Vol. 90 (1980), No. 2, 397–409

A regular semigroup S with a commutative subsemigroup of idempotents E is called weakly inverse if for any a S the set Ea of inverses aof a for which aa E is nonempty and for all, a,b S, Eab EbEa and Ea = Eb a = b. In this paper we show that in a weakly inverse semigroup S with partial identities the -class R which contains the partial identities is a right skew semigroup and conversely, every right skew semigroup R may be so represented. If R satisfies the condition that for every a,b R there exists a c R such that Ra Rb = Rc, then our considerations lead to a construction of bisimple weakly inverse semigroup with partial identities.

Mathematical Subject Classification 2000
Primary: 20M10
Received: 8 April 1977
Revised: 29 August 1979
Published: 1 October 1980
S. Madhavan