Gelfand-Kirillov dimension of some primitive abundant semigroups

Abstract

In this paper, the growth and Gelfand-Kirillov dimension of some primitive abundant semigroups are investigated. It is shown that for certain primitive abundant (regular) semigroup S, S as well as the semigroup algebra K [S] has polynomial growth if and only if all of its cancellative submonoids (subgroups) T as well as K[T] have polynomial growth. As applications, it is shown that if S is a finitely generated primitive inverse monoid having the permutational property, then clK dim K[S] = GK dim K[S] = rk(S). © 2013 The Indian National Science Academy.