On semigroup's admitting ring structure.
In this paper we introduce the notion of the structure space of -semigroups formed by the class of uniformly strongly prime ideals. We also study separation axioms and compactness property in this structure space.
We prove that the converse of Theorem 9 in "On generalized inverses in C*-algebras" by Harte and Mbekhta (Studia Math. 103 (1992)) is indeed true.
It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of -maher and -maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered or -maher semigroup can be embedded into an ordered group.
Let A be a finite-dimensional algebra over an algebraically closed field with radical square zero, and such that all simple A-modules have dimension at most two. We give a characterization of those A that have finitely many conjugacy classes of left ideals.
We compute the -theory of -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the -theory of these semigroup -algebras in terms of the -theory for the reduced group -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.