Bicyclic semigroup

About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.

Characters of finite inverse semigroups

Abstract: For elements of a finite inverse semigroup, an equivalence relation called p-conugacy is introduced. It is proved that for any matrix representation of a finite inverse semigroup the values of the character of the representation are equal on p-conjugate elements. The number of inequivalent irreducible matrix representations of a finite inverse semigroup over the field of complex numbers is equal to the number of classes of p-conjugate elements.

The syntactic monoid of the semigroup generated by a maximal prefix code

Abstract: In this paper we investigate the semigroup structure of the syntactic monoid Syn(C+) of C+, the semigroup generated by a maximal prefix code C for which C+ is a single class of the syntactic congruence. In particular we prove that for such a prefix code C, either Syn(C+) is a group or it is isomorphic to a special type of submonoid of G× T (R) where G is a group and T (R) is the full transformation semigroup on a set R with more than one element. From this description we conclude that Syn(C+) has a kernel J which is a right group. We further investigate separately the case when J is a right zero semigroup and the case when J is a group.

Prime Ideals of Cancellative Semigroups

Abstract: For a class of prime ideals P of a cancellative semigroup S it is shown that the factors S/P have a structure of a monomial semigroup over a group Consequences for the semigroup algebras K[S] are