JP Journal of Algebra, Number Theory and Applications
Volume 17, Issue 1, Pages 27 - 40
(May 2010)
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RIGHT WEAKLY REGULAR SEMIGROUPS
Henry E. Heatherly and Ralph P. Tucci
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Abstract: A
semigroup S is right weakly regular (r.w.r.)
if every right ideal of S is
idempotent. Various equivalent conditions to S
being r.w.r. and basic properties of r.w.r. semigroups are given. Constructions
and examples of r.w.r. semigroups are given. Properties of the class of all
r.w.r. semigroups are investigated and a radical associated with this class is
developed. Right weak regularity is investigated for the multiplicative and
adjoint semigroups of a ring and for simple and 0-simple semigroups |
Keywords and phrases: semigroups, right weakly regular, radicals, simple and 0-simple. |
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