Results 191 to 200 of about 25,785 (225)

Pure-Direct-Injective Modules

Lobachevskii Journal of Mathematics, 2022
The abstract of this paper gives a good idea of its content: ``In this paper, we study the class of modules having the property that if any pure submodule is isomorphic to a direct summand of such a module then the pure submodule is itself a direct summand. These modules are termed as pure-direct-injective modules (or pure-C2 modules).
Maurya, Sanjeev Kumar, Das, Soumitra, Alagoz, Yusuf   +2 more
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Limits of Pure-Injective Cotilting Modules

Algebras and Representation Theory, 2005
Let \(\Lambda\) be an Artin algebra and \(\text{Mod\,}\Lambda\) denotes the category of all right \(\Lambda\)-modules. Infinitely generated cotilting modules in \(\text{Mod\,}\Lambda\) were introduced by \textit{L. Angeleri Hügel} and \textit{F. U. Coelho} [Forum Math. 13, No. 2, 239-250 (2001; Zbl 0984.16009)]. In this paper, the authors study the set
Buan, Aslak Bakke, Solberg, Øyvind
openaire   +3 more sources

On pure-injective modules over pullback rings

Communications in Algebra, 2000
Let R be the pullback, in the sense of [9], of two Dedekind domains. We describe all those indecomposable pure-injective R-modules M with finite-dimensional top, that is, such that M/Rad(R)M is finite dimensional over R/Rad(R).
Shahabaddin Ebrahimi Atani
openaire   +3 more sources

Pure projective, pure injective and FP-injective modules over trivial ring extensions

International Journal of Algebra and Computation, 2023
Let [Formula: see text] be a trivial extension of a ring [Formula: see text] by an [Formula: see text]-[Formula: see text]-bimodule [Formula: see text]. We first study the properties of pure projective and pure injective modules over [Formula: see text]. Then we characterize [Formula: see text]-injective modules over [Formula: see text].
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WHEN COTORSION MODULES ARE PURE INJECTIVE

Journal of Mathematical Logic, 2009
We characterize rings over which every cotorsion module is pure injective (Xu rings) in terms of certain descending chain conditions and the Ziegler spectrum, which renders the classes of von Neumann regular rings and of pure semisimple rings as two possible extremes. As preparation, descriptions of pure projective and Mittag–Leffler preenvelopes with
Herzog, Ivo, Rothmaler, Philipp
openaire   +1 more source

Absolutely Pure Modules and Locally Injective Modules

2023
Goro Azumaya asked the following question: if every absolutely pure left module over a ring R is locally injective, is R left Noetherian? The technique the authors’ make use of is to study the notions of absolutely pure module and locally injective module over almost maximal valuation domains.
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n-COTILTING MODULES AND PURE-INJECTIVITY

Bulletin of the London Mathematical Society, 2004
In [J. Algebra 273, No. 1, 359-372 (2004; Zbl 1051.16007)], the author studied generalizations of the definitions of \(1\)-tilting and \(1\)-cotilting for infinitely generated modules over general rings to modules of higher projective dimension. A left \(R\)-module \(C\) is \(n\)-cotilting if (1) \(C\) has injective dimension \(\leq n\), (2) \(\text ...
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Pure-injectivity of Tensor Products of Modules

Algebra Colloquium, 2014
A classical question of Yoneda asks when the tensor product of two injective modules is injective. A complete answer to this question was given by Enochs and Jenda in 1991. In this paper the analogue question for pure-injective modules is studied.
Pournaki, M. R., Torrecillas, Blas, Tousi, M., Yassemi, Siamak   +3 more
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SUPERDECOMPOSABLE PURE INJECTIVE MODULES OVER COMMUTATIVE NOETHERIAN RINGS

Journal of Algebra and Its Applications, 2008
We investigate width and Krull–Gabriel dimension over commutative Noetherian rings which are "tame" according to the Klingler–Levy analysis in [4–6], in particular over Dedekind-like rings and their homomorphic images. We show that both are undefined in most cases.
PUNINSKAYA V., TOFFALORI, Carlo
openaire   +3 more sources

PURE-INJECTIVE MODULES NEED NOT BE RD-INJECTIVE

Quaestiones Mathematicae, 1986
Abstract It is shown that if R is a GCD domain which is not Bezout, then there exist pure-injective R-modules which are not RD-injective.
C. G. Naudé, G. Naudé, L. M. Pretorius
openaire   +1 more source