Abstract
In this paper we characterize Archimedean semigroups with idempotents satisfying (xy)m = xmym as exactly those semigroups which are a retract extension of a completely simple semigroup satisfying (xy)m = xmym by a nil semigroup satisfying (xy)m = xmym. Regular semigroups satisfying (xy)2 = x2y2 are exactly those semigroups which are a spined product of a band and a semigroup which is a semilattice of Abelian groups. A semigroup which is a nil extension of a regular semigroup satisfies (xy)2 = x2y2 if and only if it is a retract extension of a regular semigroup satisfying (xy)2 = x2y2 by a nil semigroup satisfying (xy)2 = x2y2
Original language | English (US) |
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Pages (from-to) | 332-346 |
Number of pages | 15 |
Journal | Semigroup Forum |
Volume | 8 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1974 |
ASJC Scopus subject areas
- Mathematics(all)