منابع مشابه
AGQP-Injective Modules
Let R be a ring and let M be a right R-module with S End MR . M is called almost general quasiprincipally injective or AGQP-injective for short if, for any 0/ s ∈ S, there exist a positive integer n and a left ideal Xsn of S such that s / 0 and lS Ker s Ss ⊕ Xsn . Some characterizations and properties of AGQP-injective modules are given, and some properties of AGQP-injective modules with additi...
متن کاملGeneralizations of principally quasi-injective modules and quasiprincipally injective modules
LetR be a ring andM a rightR-module with S= End(MR). The moduleM is called almost principally quasi-injective (or APQ-injective for short) if, for any m∈M, there exists an S-submodule Xm of M such that lMrR(m) = Sm ⊕ Xm. The module M is called almost quasiprincipally injective (or AQP-injective for short) if, for any s∈ S, there exists a left ideal Xs of S such that lS(ker(s)) = Ss ⊕ Xs. In thi...
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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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$R$-module. In this paper, we explore more properties of $Max$-injective modules and we study some conditions under which the maximal spectrum of $M$ is a $Max$-spectral space for its Zariski topology.
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We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisely the generization closed subsets of the spectrum of the ring.
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2008
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2008/469725