Results 201 to 210 of about 28,036 (238)

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
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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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SUPERDECOMPOSABLE PURE-INJECTIVE MODULES AND INTEGRAL GROUP RINGS

Journal of the London Mathematical Society, 2006
We prove that if G is a non-trivial finite group, then the integral group ring ℤG possesses a superdecomposable pure-injective module. © 2006 London Mathematical Society.
Puninskiy, Gennady, Puninski, Gena, Puninskaya, Vera, Toffalori, Carlo   +3 more
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∑-Pure-Injective Modules Over Serial Rings

1995
We prove that every ∑-pure-injective module over a serial ring is serial and every ∑-pure-injective faithful indecomposable module over a serial ring is ∑-injective. Moreover, every serial ring that can be realized as the endomorphism ring of an artinian module has finite Krull dimension.
Alberto Facchini, Gennadi Puninski
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Indecomposable decompositions of pure-injective modules

Communications in Algebra, 1998
(1998). Indecomposable decompositions of pure-injective modules. Communications in Algebra: Vol. 26, No. 11, pp. 3709-3725.
openaire   +1 more source

On Pure-Injective Modules

1984
Some results on pure-injective modules over a commutative ring with 1, proved by Ziegler using model theory, are proved here through algebraic methods. As application of these results we obtain again the structure of indecomposable pure-injective modules over a valuation domain, showing that their elements have constant indicator.
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Pure Injective Modules over a Commutative Valuation Domain

Algebras and Representation Theory, 2003
This paper brings the problem of classification of pure injective modules over a commutative valuation domain (CVD) closer to its conclusion by classifying those pure injective modules over a CVD which are envelopes \(N(m)\) of one element \(m\). Geometrical invariants and methods are used.
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Σ-pure-injective Modules and Artinian Modules

1998
The aim of this chapter is to study the endomorphism rings of artinian modules (Section 10.2) and, in particular, to characterize the endomorphism rings of artinian modules that are serial rings (Theorem 10.23). If M S is an artinian module over an arbitrary ring S and R = End(M S ), then R MS is a bimodule and RM is a faithful Σ-pure-injective module (
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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).
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