Displaying similar documents to “A note on isomorphic commutative group algebras over certain rings.”

Isomorphism of commutative group algebras of p -mixed splitting groups over rings of characteristic zero

Peter Vassilev Danchev (2006)

Mathematica Bohemica

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Suppose G is a p -mixed splitting abelian group and R is a commutative unitary ring of zero characteristic such that the prime number p satisfies p ∉ inv ( R ) ∪ zd ( R ) . Then R ( H ) and R ( G ) are canonically isomorphic R -group algebras for any group H precisely when H and G are isomorphic groups. This statement strengthens results due to W. May published in J. Algebra (1976) and to W. Ullery published in Commun. Algebra (1986), Rocky Mt. J. Math. (1992) and Comment. Math. Univ. Carol. (1995).

Torsion units in group rings.

Vikas Bist (1992)

Publicacions Matemàtiques

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Let U(RG) be the unit group of the group ring RG. In this paper we study group rings RG whose support elements of every torsion unit are torsion, where R is either the ring of integers Z or a field K.