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

Ullery, William. "A note on group algebras of $p$-primary abelian groups." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 11-14. <http://eudml.org/doc/247776>.

@article{Ullery1995,
abstract = {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 $RG$ and $RH$ are $R$-isomorphic. Under certain restrictions on the ideal structure of $R$, it is shown that $G$ and $H$ are isomorphic.},
author = {Ullery, William},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {commutative group algebras; isomorphism; isomorphism problem; group algebras; Abelian -groups},
language = {eng},
number = {1},
pages = {11-14},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on group algebras of $p$-primary abelian groups},
url = {http://eudml.org/doc/247776},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Ullery, William
TI - A note on group algebras of $p$-primary abelian groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 1
SP - 11
EP - 14
AB - 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 $RG$ and $RH$ are $R$-isomorphic. Under certain restrictions on the ideal structure of $R$, it is shown that $G$ and $H$ are isomorphic.
LA - eng
KW - commutative group algebras; isomorphism; isomorphism problem; group algebras; Abelian -groups
UR - http://eudml.org/doc/247776
ER -