JP Journal of Algebra, Number Theory and Applications
Volume 19, Issue 1, Pages 1 - 12
(November 2010)
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WEAK REGULARITY IN SEMIGROUPS
Henry E. Heatherly and Ralph P. Tucci
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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.