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JP Journal of Algebra, Number Theory and Applications

and

be the multiplicative semigroups of all right (left) ideals of a semigroup S. This paper investigates the structure of

and

and the relation to the structure of S. Various semilattice decompositions and some permutation identity conditions are considered. A semigroup S is right weakly p-regular (r.w.p.r.) if for each

there is some n such that the right ideal generated by

is idempotent. Such semigroups are investigated and a radical associated with the r.w.p.r. property is developed. Connections are made between various weak regularity conditions.

JP Journal of Algebra, Number Theory and Applications
Volume 19, Issue 1, Pages 1 - 12 (November 2010)

WEAK REGULARITY IN SEMIGROUPS
Henry E. Heatherly and Ralph P. Tucci

Abstract:
Let

and

be the multiplicative semigroups of all right (left) ideals of a semigroup S. This paper investigates the structure of

and

and the relation to the structure of S. Various semilattice decompositions and some permutation identity conditions are considered. A semigroup S is right weakly p-regular (r.w.p.r.) if for each

there is some n such that the right ideal generated by

is idempotent. Such semigroups are investigated and a radical associated with the r.w.p.r. property is developed. Connections are made between various weak regularity conditions.

Keywords and phrases: semigroups, weakly regular, permutation identity, radicals, p-regular.

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