Cyclic Injective Modules of Full Linear Rings
نویسندگان
چکیده
منابع مشابه
Injective Modules and Fp-injective Modules over Valuation Rings
It is shown that each almost maximal valuation ring R, such that every indecomposable injective R-module is countably generated, satisfies the following condition (C): each fp-injective R-module is locally injective. The converse holds if R is a domain. Moreover, it is proved that a valuation ring R that satisfies this condition (C) is almost maximal. The converse holds if Spec(R) is countable....
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It is proved that EJ is injective if E is an injective module over a valuation ring R, for each prime ideal J 6= Z. Moreover, if E or Z is flat, then EZ is injective too. It follows that localizations of injective modules over h-local Prüfer domains are injective too. If S is a multiplicative subset of a noetherian ring R, it is well known that SE is injective for each injective R-module E. The...
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It is proved that localizations of injective R-modules of finite Goldie dimension are injective if R is an arithmetical ring satisfying the following condition: for every maximal ideal P , RP is either coherent or not semicoherent. If, in addition, each finitely generated R-module has finite Goldie dimension, then localizations of finitely injective R-modules are finitely injective too. Moreove...
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Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated R-modules. For any n 0, we prove that R is a Gorenstein ring with self-injective dimension at most n if and only if every finitely generated left R-module and every finitely generated right R-module have torsionfree dimension at most n, if and only if every finitely generated le...
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It is proven that the weak dimension of each FP-injective module over a chain ring which is either Archimedean or not semicoherent is less or equal to 2. This implies that the projective dimension of any countably generated FP-injective module over an Archimedean chain ring is less or equal to 3. By [7, Theorem 1], for any module G over a commutative arithmetical ring R the weak dimension of G ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1966
ISSN: 0002-9939
DOI: 10.2307/2035099