Results 11 to 20 of about 28,036 (238)
Some criteria of cyclically pure injective modules
Journal of Algebra, 2006 The structure of cyclically pure injective modules over a commutative ring $R$ is investigated and several characterizations for them are presented. In particular, we prove that a module $D$ is cyclically pure injective if and only if $D$ is isomorphic to a direct summand of a module of the form $\Hom_R(L,E)$ where $L$ is the direct sum of a family of ...
Divaani-Aazar, Kamran +2 more
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Rings whose pure-injective right modules are direct sums of lifting modules
Journal of Algebra, 2013 A module \(M\) is called a lifting module if for every submodule \(N\) of \(M\), there exists a direct sum decomposition \(M=M_1\oplus M_2\) with \(M_1\subseteq N\) and \(N\cap M_2\) superfluous in \(M_2\). These modules are dual to the notion of extending (also called, CS) modules.
Guil Asensio, Pedro A. +1 more
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Two characterizations of pure injective modules [PDF]
Proceedings of the American Mathematical Society, 2006 Let R R be a commutative ring with identity and D D an R R -module. It is shown that if D D is pure injective, then D D is isomorphic to a direct summand of the direct product of a family of finitely embedded modules.
Kamran Divaani-Aazar +2 more
openaire +1 more source
Maranda’s theorem for pure-injective modules and duality
Canadian Journal of Mathematics, 2022 AbstractLet R be a discrete valuation domain with field of fractions Q and maximal ideal generated by $\pi $ . Let $\Lambda $ be an R-order such that $Q\Lambda $ is a separable Q-algebra. Maranda showed that there exists $k\in \mathbb {N}$ such that for all $\Lambda $ -lattices L and M, if $L/L\pi ^k\simeq M/M\pi ^k$ , then $L\simeq M ...
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Σ-pure-injective modules for string algebras and linear relations [PDF]
Journal of Algebra, 2018 We prove that indecomposable $ $-pure-injective modules for a string algebra are string or band modules. The key step in our proof is a splitting result for infinite-dimensional linear relations.
Raphael Bennett-Tennenhaus +1 more
openaire +4 more sources
Module categories for group algebras over commutative rings [PDF]
, 2012 We develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the finitely ...
Benson, Dave +3 more
core +2 more sources
Gorenstein injective envelopes and covers over two sided noetherian rings [PDF]
, 2016 We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat.
Iacob, Alina
core +3 more sources
, 2016 We investigate the properties of pure derived categories of module categories, and show that pure derived categories share many nice properties of classical derived categories.
Huang, Zhaoyong, Zheng, Yuefei
core +1 more source
, 2011 In this paper, we give some characterizations of FP-grinjective R-modules and graded right R-modules of FP-gr-injective dimension at most n. We study the existence of FP-gr-injective envelopes and FP-gr-injective covers.
Liu, Zhongkui, Yang, Xiaoyan
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Modules with RD-composition series over a commutative ring [PDF]
, 2003 If R is a commutative ring, we prove that every finitely generated module has a pure-composition series with indecomposable factors and any two such series are isomorphic if and only if R is a Bezout ring and a CF ...
Couchot, Francois
core +4 more sources