Clarke and Monzo defined in [3] a construction called a generalized inflation of a semigroup. It is always the case that any inflation of a semigroup is a generalized inflation, and any generalized inflation of a semigroup is a null extension of the semigroup. Clarke and Monzo proved that any associative null extension of a base semigroup which is a union of groups is in fact a generalized inflation. In this paper we study null extensions and generalized inflations of Brandt semigroups. We first prove that any generalized inflation of a Brandt semigroup is actually an inflation of the semigroup. This answers a question posed by Clarke and Monzo in [3]. Then we characterize associative null extensions of Brandt semigroups, and show that there are associative null extensions of Brandt semigroups which are not generalized inflations.

Additional Metadata
Keywords Brandt semigroups, Generalized inflation, Inflation, Null extension
Persistent URL dx.doi.org/10.1007/s00233-006-0663-9
Journal Semigroup Forum
Citation
Wang, Q, & Wismath, S.L. (2007). Null extensions and generalized inflations of brandt semigroups. Semigroup Forum, 74(2), 274–292. doi:10.1007/s00233-006-0663-9