Vol. 41, No. 2, 1972

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Period H-semigroups and t-semisimple periodic H-semigroups

Mary Joel Jordan

Vol. 41 (1972), No. 2, 437–446

An H-semigroup is a semigroup such that every right and every left congruence is a two-sided congruence on the semigroup. It is known that the set of idempotents of an H-semigroup form a subsemigroup. A semigroup is t-semisimple provided the intersection of all its maximal modular congruences is the identity relation. Let S be a periodic H-semigroup such that the subsemigroup E of idempotents of S is commutative. In this paper it is shown that S is a semilattice of disjoint one-idempotent H-semigroups, and that every subgroup of S is a Hamiltonian group. Moreover, if S is t-semisimple, then S is an inverse semigroup such that the oneridempotent H-semigroups of the semilattice are the maximal subgroups of S, and a complete characterization is given.

Mathematical Subject Classification 2000
Primary: 20M10
Received: 25 July 1970
Revised: 16 June 1971
Published: 1 May 1972
Mary Joel Jordan