Open AccessON IDEALS OF THE COEFFICIENT RINGS IN GROUP RINGS
Author(s) -
Sushma Saini
Publication year - 1994
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.25.1994.4442
Subject(s) - mathematics , abelian group , group (periodic table) , group ring , pure mathematics , semiprime ring , combinatorics , prime (order theory) , chemistry , organic chemistry
Let $R$ and $S$ be rings, $G$ any group. If the group rings $RG$ and $SG$ are isomorphic as rings, we formulate a correspondence between the ideals of $R$ and those of $S$ and show that this correspondence is one-to-one in case $R$ and $S$ are isomorphic. It is shown that this correspondence also works for Jordan ideals, provided that $G$ is abelian.