Results 11 to 20 of about 25,785 (225)
On locally pure-injective modules
Journal of Pure and Applied Algebra, 2002 A submodule \(M\) of a right \(R\)-module \(N\) is called strongly pure (s-pure) if for every finite tuple \(x_1,x_2,\dots,x_n\) of elements of \(M\) there exists a map \(t\in\Hom(N,M)\) such that \(t(x_i)=x_i\) for \(1\leq i\leq n\). A monomorphism \(f\colon M\to N\) is called s-pure if \(f(M)\) is s-pure in \(N\).
openaire +4 more sources
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
openaire +5 more sources
Minimal pure injective resolutions of flat modules
Journal of Algebra, 1987 This paper examines the pure injective minimal resolution of a flat module F over a noetherian ring R. Starting from the fact that the pure injective envelope \(PE(F)\) of a flat module F over a noetherian ring \(R\) can be represented as: \(PE(F)=\oplus_{{\mathfrak p}\in\text{Spec} k}T_{{\mathfrak p}}\), where \(T_{{\mathfrak p}}\) is the completion ...
openaire +4 more sources
Glasgow Mathematical Journal, 1973 AbstractIt is proved that a pure-injective module over a commutative ring with unity is a summand of a product of duals of finitely presented modules, where duals are to be understood with reference to the circle group T, with induced module structures.
openaire +1 more source
Ringel's conjecture for domestic string algebras [PDF]
, 2015 We classify indecomposable pure injective modules over domestic string algebras, verifying Ringel's conjecture on the structure of such modules.Comment: minor ...
Prest, Mike, Puninski, Gena
core +2 more sources
Submodules of secondary modules
International Journal of Mathematics and Mathematical Sciences, 2002 Let R be a commutative ring with nonzero identity. Our objective is to investigate representable modules and to examine in particular when submodules of such modules are representable. Moreover, we establish a connection between the secondary modules and
Shahabaddin Ebrahimi Atani
doaj +1 more source
Extensions of three classical theorems to modules with maximum condition for finite matrix subgroups [PDF]
, 1998 In this article analogues of the Hilbert Basis Theorem, the Artin-Rees Lemma and the Krull Intersection Theorem are shown for modules with ascending chain condition for finite matrix subgroups.
Zimmermann, Wolfgang
core +1 more source
Tilting and cotilting modules over concealed canonical algebras [PDF]
, 1996 We study infinite dimensional tilting modules over a concealed canonical algebra of domestic or tubular type. In the domestic case, such tilting modules are constructed by using the technique of universal localization, and they can be interpreted in ...
Hügel, Lidia Angeleri, Kussin, Dirk
core +6 more sources
On (co)pure Baer injective modules [PDF]
Algebra and Discrete Mathematics, 2021 For a given class of R-modules Q, a module M is called Q-copure Baer injective if any map from a Q-copure left ideal of R into M can be extended to a map from R into M. Depending on the class Q, this concept is both a dualization and a generalization of pure Baer injectivity. We show that every module can be embedded as Q-copure submodule of a Q-copure
openaire +3 more sources
, 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
core +1 more source