Geodesic
Isomorphic Group Rings Over Domains
Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 85-89

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DOI

Let R and S be rings, G and H abelian groups, and RG and SH the goup rings of G and H over R and S respectively. In this note we consider what relations must hold between G and H or between R and S if the group rings RG and SH are isomorphic. For example, it is shown that if R and S are integral domains of characteristic zero, G and H torsion abelian groups such that if G has an element of order p then p is not invertible in R, and RG and SH are isomorphic, then the rings R and 5 are isomorphic and the groups G and H are isomorphic.
DOI : 10.4153/CMB-1989-012-6
Mots-clés : 16A27 
Adjaero, Isabelle; Spiegel, Eugene. Isomorphic Group Rings Over Domains. Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 85-89. doi: 10.4153/CMB-1989-012-6
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     author = {Adjaero, Isabelle and Spiegel, Eugene},
     title = {Isomorphic {Group} {Rings} {Over} {Domains}},
     journal = {Canadian mathematical bulletin},
     pages = {85--89},
     year = {1989},
     volume = {32},
     number = {1},
     doi = {10.4153/CMB-1989-012-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-012-6/}
}
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