Gelfand-Kirillov Dimension of Noetherian Semigroup Algebras

AbstractIt is shown that for certain classes of semigroup algebras K[S], including right noetherian algebras, the Gelfand-Kirillov dimension is finite whenever it is finite on all cancellative subsemigroups of S. Moreover, the dimension of the algebra modulo the prime radical is then an integer. A description of cancellative semigroups of polynomial growth, extending Gromov′s theorem, has been recently obtained by Grigorchuk. Some bounds on GK(K[S]) are determined. Our approach is based on the structure of the image S of S modulo the prime radical of K[S], on the correspondence between the cancellative subsemigroups in S and S and on Grigorchuk′s result