On regular semigroups and their multiplication.
Let be a regular semigroup and be the set of its idempotents. We call the sets and one-sided sandwich sets and characterize them abstractly where . For such that , , we call the sandwich set of . We characterize regular semigroups in which all (or all are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural order. For every , we also define as the set of all idempotets such that, for any congruence on...
We give a new condition on a monoid M for the monoid ring F[M] to be a 2-fir. Furthermore, we construct a monoid M that satisfies all the currently known necessary conditions for F[M] to be a semifir and that the group of units of M is trivial, but M is not a directed union of free monoids.