Results 1  10
of
9,299
On group rings with involution
"... Abstract. In this note, we consider the involution group ring AG of an involution group G over an involution ring A with identity and prove the involutive version of a Theorem due to Connell, which characterizes *artinian group rings with identity. Furthermore, *simple involution group rings are ..."
Abstract
 Add to MetaCart
Abstract. In this note, we consider the involution group ring AG of an involution group G over an involution ring A with identity and prove the involutive version of a Theorem due to Connell, which characterizes *artinian group rings with identity. Furthermore, *simple involution group rings
Invariants of group rings
, 1988
"... The Schur group, uniform (distribution) group, Schur index, and Schur exponent are examined in the context of separable group rings of finite groups over commutative rings. ..."
Abstract
 Add to MetaCart
The Schur group, uniform (distribution) group, Schur index, and Schur exponent are examined in the context of separable group rings of finite groups over commutative rings.
Twisted group rings
 Comm. Alg
, 1989
"... This paper deals with (twisted) Hopf algebra forms of group rings, i.e. with Hopf algebrasH over a base ringK, such that for a suitable extension L of K the Hopf algebra L ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This paper deals with (twisted) Hopf algebra forms of group rings, i.e. with Hopf algebrasH over a base ringK, such that for a suitable extension L of K the Hopf algebra L
SKEW GROUP RINGS
, 1978
"... Let R be a ring and G a group, and suppose there is a group homomorphism, s, from G to the group of automorphisms of R. We may form the skew group ring RsG, by imposing the multiplication rg = gr s(g) on the free (right) Rmodule with basis G. Very often the map s will be an embedding in this case ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Let R be a ring and G a group, and suppose there is a group homomorphism, s, from G to the group of automorphisms of R. We may form the skew group ring RsG, by imposing the multiplication rg = gr s(g) on the free (right) Rmodule with basis G. Very often the map s will be an embedding
Isomorphic groups and group rings
 Pacific J. Math
, 1965
"... Abstract. This paper consists of two parts. The first is concerned with free products in linear groups and uses the usual “ping pong ” lemma and attractors to prove the results. What is new here is that we allow certain subspaces of V associated with the semisimple and generalized transvection opera ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
operators to have dimensions larger than 1. The second part is concerned with applications of this machinery to integral groups rings Z[G] of finite groups. We show, for example, that if G is nonabelian of order prime to 6, then Z[G] contains two Bass cyclic units that generate a nonabelian free group. 1
NONCOMMUTATIVE LOCALIZATION IN GROUP RINGS
, 2003
"... Abstract. This paper will briefly survey some recent methods of localization in group rings, which work in more general contexts than the classical Ore localization. In particular the Cohn localization using matrices will be described, but other methods will also be considered. 1. ..."
Abstract
 Add to MetaCart
Abstract. This paper will briefly survey some recent methods of localization in group rings, which work in more general contexts than the classical Ore localization. In particular the Cohn localization using matrices will be described, but other methods will also be considered. 1.
Groups, Rings and Fields
"... These notes give an introduction to the basic notions of abstract algebra, groups, rings (so far as they are necessary for the construction of field extensions) and Galois theory. Each section is followed by a series of problems, partly to check understanding (marked with the letter “R”: Recommende ..."
Abstract
 Add to MetaCart
These notes give an introduction to the basic notions of abstract algebra, groups, rings (so far as they are necessary for the construction of field extensions) and Galois theory. Each section is followed by a series of problems, partly to check understanding (marked with the letter “R
On group rings with restricted minimum condition
, 2007
"... In this paper we investigate the group rings RG satisfying the restricted minimum condition. ..."
Abstract
 Add to MetaCart
In this paper we investigate the group rings RG satisfying the restricted minimum condition.
NORMALITY IN GROUP RINGS
, 804
"... Abstract. Let KG be the group ring of a group G over a commutative ring K with unity. The rings KG are described for which xxσ = xσx for all x = P g∈G αgg ∈ KG, where x ↦ → xσ = P g∈G αgf(g)σ(g) is an involution of KG; here f: G → U(K) is a homomorphism and σ is an antiautomorphism of order two of ..."
Abstract
 Add to MetaCart
Abstract. Let KG be the group ring of a group G over a commutative ring K with unity. The rings KG are described for which xxσ = xσx for all x = P g∈G αgg ∈ KG, where x ↦ → xσ = P g∈G αgf(g)σ(g) is an involution of KG; here f: G → U(K) is a homomorphism and σ is an antiautomorphism of order two
Idempotents in group rings
 Duke Math. J
, 1964
"... Introduction. Suppose G is a group and R is a ring. The support of a function f from G to R is the set of all x e G at which f(x) ~ O. The support group of f is the smallest subgroup of G which contains the support of f. The group ring RG is the set of all Rvalued functions on G whose support is f ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Introduction. Suppose G is a group and R is a ring. The support of a function f from G to R is the set of all x e G at which f(x) ~ O. The support group of f is the smallest subgroup of G which contains the support of f. The group ring RG is the set of all Rvalued functions on G whose support
Results 1  10
of
9,299