Vol. 85, No. 2, 1979

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ISSN: 0030-8730
Right subdirectly irreducible semigroups

Stuart Rankin, Clive Reis and Gabriel Thierrin

Vol. 85 (1979), No. 2, 403–412
Abstract

It is well-known that a semigroup is subdirectly irreducible if and only if it has a minimum nontrivial congruence. From this point of view, it is natural to call a semigroup right (left) subdirectly irreducible if and only if it has a minimum nontrivial right (left) congruence. It turns out that such semigroups are exactly the subdirectly irreducible semigroups for which the minimum nontrivial congruence is also a minimum nontrivial right (left) congruence. These semigroups form a class of subdirectly irreducible semigroups for which results similar to those obtained by Schein for commutative subdirectly irreducible semigroups are obtained. In fact, since a commutative semigroup is subdirectly irreducible if and only if it is right subdirectly irreducible, some of the results of this paper offer additional knowledge on the structure of subdirectly irreducible semigroups of the third kind.

Mathematical Subject Classification 2000
Primary: 20M10
Milestones
Received: 14 June 1976
Published: 1 December 1979
Authors
Stuart Rankin
Clive Reis
Gabriel Thierrin