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2012•Journal of MathematicsRequires access

ON WEAKLY L-REGULAR SEMIGROUPS WITH CENTRAL IDEMPOTENTS

Gong Chunmei

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Abstract

Weakly L-regular semigroups with central idempotents are introduced and their algebraic structures are studied in this paper.By using a right congruence L+ and a left congruence R+ on a semigroup S,respectively,we show that a semigroup S is a weakly L-regular semigroup with central idempotents if and only if S is a strong semilattice of H-left cancellative monoids,which generalizes the corresponding results of Clifford semigroups in the class of regular semigroups.

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What this paper is about

Weakly L-regular semigroups with central idempotents are introduced and their algebraic structures are studied in this paper.By using a right congruence L+ and a left congruence R+ on a semigroup S,respectively,we show that a semigroup S is a weakly L-regular semigroup with central idempotents if and only if S is a strong semilattice of H-left cancellative monoids,which generalizes the corresponding results of Clifford semigroups in the class of regular semigroups.

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Available abstract

Weakly L-regular semigroups with central idempotents are introduced and their algebraic structures are studied in this paper.By using a right congruence L+ and a left congruence R+ on a semigroup S,respectively,we show that a semigroup S is a weakly L-regular semigroup with central idempotents if and only if S is a strong semilattice of H-left cancellative monoids,which generalizes the corresponding results of Clifford semigroups in the class of regular semigroups.

Key concepts: Mathematics, Semilattice, Congruence (geometry), Semigroup, Pure mathematics, Regular semigroup, Cancellative semigroup, Algebraic number

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