Normalizers and Free Groups in the Unit Group of an Integral Semigroup Ring

Abstract

In this article, we introduce the normalizer N U (R) (X) of a subset X of a ring R (with identity) in the unit group U (R) and consider, in particular, the normalizer of the natural basis ±S of the integral semigroup ring Z 0 S of a finite semigroup S. We investigate properties of this normalizer for the class of semigroup rings of inverse semigroups, which contains, for example, matrix rings, in particular, matrix rings over group rings, and partial group rings. We also construct free groups in the unit group of an integral semigroup ring of a Brandt semigroup using a bicyclic unit.

Recent developments around partial actions

“…More information around partial actions may be found in the surveys [45,115,116,170,250,251,260]. Notice also that partial actions and/or related structures have been mentioned in [12,13,24,46,62,67,90,92,142,154,161,166,167].…”

Recent developments around partial actions

“…Notice also that partial actions and/or related structures have been mentioned in [12], [13], [24], [46], [62], [67], [90], [92], [142], [154], [161], [167] and [166].…”