Results 11 to 20 of about 25,785 (225)
On Wild Algebras and Super-Decomposable Pure-Injective Modules [PDF]
Algebras and Representation Theory, 2022 AbstractAssume that k is an algebraically closed field and A is a finite-dimensional wild k-algebra. Recently, L. Gregory and M. Prest proved that in this case the width of the lattice of all pointed A-modules is undefined. Hence the result of M. Ziegler implies that there exists a super-decomposable pure-injective A-module, if the base field k is ...
Grzegorz Pastuszak
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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 \(N\).
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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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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 ...
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International Journal of Mathematics and Mathematical Sciences, 1997 In this paper we generalize the notion of pure injectivity of modules by introducing what we call a pure Baer injective module. Some properties and some characterization of such modules are established.
Nada M. Al Thani
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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
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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
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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
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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
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