Turkish Journal of Mathematics
Abstract
Let K be a field and let G be a group. If G acts on an abelian group V, then it acts naturally on any group algebra K[V], and we are concerned with classifying the G-stable ideals of K[V]. In this paper, we consider a rather concrete situation. We take G to be an infinite locally finite simple group acting in a finitary manner on V. When G is a finitary version of a classical linear group, then we show that the augmentation ideal \omega K[G] is the unique proper G-stable ideal of K[V]. On the other hand, if G is a finitary alternating group acting on a suitable permutation module V, then there is a rich family of G-stable ideals of K[V], and we show that these behave like certain graded ideals in a polynomial ring.
DOI
-
Keywords
group algebra, invariant ideal, locally finite simple group, finitary permutation group, permutation module, finitary linear group
First Page
113
Last Page
130
Recommended Citation
PASSMAN, D. S (2007). Finitary Actions and Invariant Ideals. Turkish Journal of Mathematics 31 (5): 113-130. https://doi.org/-
