منابع مشابه
On generalizations of semiperfect and perfect rings
We call a ring $R$ right generalized semiperfect if every simple right $R$-module is an epimorphic image of a flat right $R$-module with small kernel, that is, every simple right $R$-module has a flat $B$-cover. We give some properties of such rings along with examples. We introduce flat strong covers as flat covers which are also flat $B$-covers and give characterizations of $A$-perfe...
متن کاملon generalizations of semiperfect and perfect rings
we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel, that is, every simple right $r$-module has a flat $b$-cover. we give some properties of such rings along with examples. we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...
متن کاملOn n-Perfect Rings and Cotorsion Dimension
A ring is called n-perfect (n ≥ 0), if every flat module has projective dimension less or equal than n. In this paper, we show that the n-perfectness relate, via homological approach, some homological dimension of rings. We study n-perfectness in some known ring constructions. Finally, several examples of n-perfect rings satisfying special conditions are given.
متن کاملOn Regular Group Rings
Let G be a multiplicative group, K a commutative ring with unit, and K(G) the group ring of G with respect to K. We say that K(G) is regular if given an x in K(G), there is a y in K(G) such that xyx = x. Using a homological characterization of regular rings which was found independently by M. Harada [2, Theorem 5] and the author, we prove that if G is locally finite, then K(G) is regular if and...
متن کاملCOTORSION DIMENSIONS OVER GROUP RINGS
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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0271247-4