Isomorphic group rings over domains revisited
نویسندگان
چکیده
منابع مشابه
A Note on Isomorphic Commutative Group Algebras over Certain Rings
Suppose G is an abelian group and R is a commutative ring with 1 of char(R) = 0. It is proved that if G is R-favorable torsion and RH and RG are R-isomorphic group algebras for some group H , then H is Rfavorable torsion abelian if and only if either inv(R) = ∅ or inv(R) = ∅ and R is an ND-ring. This strengthens results due to W. Ullery (Comm. Algebra, 1986), (Rocky Mtn. J. Math., 1992) and (Co...
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Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.
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Let $(R, m)$ be a commutative noetherian local ring and let $Gamma$ be a finite group. It is proved that if $R$ admits a dualizing module, then the group ring $Rga$ has a dualizing bimodule as well. Moreover, it is shown that a finitely generated $Rga$-module $M$ has generalized Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero as an $R$-module.
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A full classification up to isomorphism of torsions in abelian group rings over an algebraically closed field of nonzero characteristic is given in the present article. Specifically, an explicit formula is established and so the problem is completely exhausted. This characterizing strengthens classical results in that aspect due to Chatzidakis-Pappas (J. London Math. Soc., 1991) and to the auth...
متن کاملDo Isomorphic Structural Matrix Rings Have Isomorphic Graphs?
We first provide an example of a ring R such that all possible 2 × 2 structural matrix rings over R are isomorphic. However, we prove that the underlying graphs of any two isomorphic structural matrix rings over a semiprime Noetherian ring are isomorphic, i.e. the underlying Boolean matrix B of a structural matrix ring M(B,R) over a semiprime Noetherian ring R can be recovered, contrary to the ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1990
ISSN: 0021-8693
DOI: 10.1016/0021-8693(90)90234-f