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A direct factor theorem for commutative group algebras

William Ullery (1992)

Commentationes Mathematicae Universitatis Carolinae

Suppose $F$ is a field of characteristic $p \neq 0$ and $H$ is a $p$ -primary abelian $A$ -group. It is shown that $H$ is a direct factor of the group of units of the group algebra $F H$ .

A generalized Hopf formula for higher homology groups.

Ralph Stöhr (1989)

Commentarii mathematici Helvetici

A geometric invariant for modules over an Abelian group.

Robert Bieri, Ralph Strebel (1981)

Journal für die reine und angewandte Mathematik

A Kirillov theory for divisible nilpotent groups.

A.L. Carey, W. Moran, C.E.M. Pearce (1995)

Mathematische Annalen

A note on group algebras of $p$ -primary abelian groups

William Ullery (1995)

Commentationes Mathematicae Universitatis Carolinae

Suppose $p$ is a prime number and $R$ is a commutative ring with unity of characteristic 0 in which $p$ is not a unit. Assume that $G$ and $H$ are $p$ -primary abelian groups such that the respective group algebras $R G$ and $R H$ are $R$ -isomorphic. Under certain restrictions on the ideal structure of $R$ , it is shown that $G$ and $H$ are isomorphic.

A note on isomorphic commutative group algebras over certain rings.

Danchev, Peter (2005)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

A note on semilocal group rings

Angelina Y. M. Chin (2002)

Czechoslovak Mathematical Journal

Let $R$ be an associative ring with identity and let $J (R)$ denote the Jacobson radical of $R$ . $R$ is said to be semilocal if $R / J (R)$ is Artinian. In this paper we give necessary and sufficient conditions for the group ring $R G$ , where $G$ is an abelian group, to be semilocal.