Let G be a multiplicative group, K a commutative ring with unit, and K (G) the group ring of G
with respect to K. We say that K (G) is regular if given an x in K (G), there is ay in K (G) such …

G=: ff 1 2 (? l 2... 2ff B 2^ 1={l} of subgroups such that, for each ie (1, 2,..., n}, Gi+ 1 is a
normal subgroup of Gi and the factor group GJGiJrX is either finite or cyclic. Let h (G) denote …

Let G be a finite group, S a commutative ring with one and S [G] the group ring of G over S. If
H is a group with G≅ H then clearly S [G]≅ S [H] where the latter is an S-isomorphism. We …

Let R be the discrete group ring of the group G over the ring A. In this paper we attempt to
find necessary and sufficient conditions on G and A so that R will have some standard ring …

In (4), Connell proved that RG is a Noetherian ring if and only if R is a Noetherian ring and G
is a finitely generated group. Motivated by this result we ask when is RG a coherent ring …

1. Introduction. Let G be a group and R a commutative ring with identity element. The group
ring r of G over R consists of all formal sums Ea (g) g where gEG, a (g) ER and a (g)= 0 …

Suppose G is a poly-(cyclic or finite) group; that is, G has a series of subgroups G= Gt 3 G2
3... 2 Gn 3 Gn+!={1} such that for each i, Gi+ x is a normal subgroup of Gj and the factor …

The purpose of this note is to generalize a result of Gulliksen, Ribenboim and Viswanathan
which characterized local group rings when both the ring and the group are commutative …

ON PERFECT GROUP RINGS Page 1 PROCEEDINGS of the AMERICAN MATHEMATICAL
SOCIETY Volume 27, Number 1, January 1971 ON PERFECT GROUP RINGS SM WOODS1 …

Let R be a commutative ring with unity and let G be a group. The group ring RG has a
natural involution that maps each element of G to its inverse. We denote by RG+ the set of …