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Displaying 201 – 220 of 242

The component quiver of a self-injective artin algebra

Alicja Jaworska, Andrzej Skowroński (2011)

Colloquium Mathematicae

We prove that the component quiver $Σ_{A}$ of a connected self-injective artin algebra A of infinite representation type is fully cyclic, that is, every finite set of components of the Auslander-Reiten quiver $Γ_{A}$ of A lies on a common oriented cycle in $Σ_{A}$ .

The existence of envelopes

Edgar E. Enochs, Overtoun M. G. Jenda, Jinzhong Xu (1993)

Rendiconti del Seminario Matematico della Università di Padova

The existence of relative pure injective envelopes

Fatemeh Zareh-Khoshchehreh, Kamran Divaani-Aazar (2013)

Colloquium Mathematicae

Let 𝓢 be a class of finitely presented R-modules such that R∈ 𝓢 and 𝓢 has a subset 𝓢* with the property that for any U∈ 𝓢 there is a U*∈ 𝓢* with U* ≅ U. We show that the class of 𝓢-pure injective R-modules is preenveloping. As an application, we deduce that the left global 𝓢-pure projective dimension of R is equal to its left global 𝓢-pure injective dimension. As our main result, we prove that, in fact, the class of 𝓢-pure injective R-modules is enveloping.

The flat dimensions of injective modules.

Nanqing Ding, Jianlong Chen (1993)

Manuscripta mathematica

The general structure of inverse polynomial modules

Sangwon Park (2001)

Czechoslovak Mathematical Journal

In this paper we compute injective, projective and flat dimensions of inverse polynomial modules as $R [x]$ -modules. We also generalize Hom and Ext functors of inverse polynomial modules to any submonoid but we show Tor functor of inverse polynomial modules can be generalized only for a symmetric submonoid.

The importance of rational extensions

Frans Loonstra (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The rational completion $\bar{M}$ of an $R$ -module $M$ can be characterized as a $\tau_{M}$ -injective hull of $M$ with respect to a (hereditary) torsion functor $\tau_{M}$ depending on $M$ . Properties of a torsion functor depending on an $R$ -module $M$ are studied.

The N*-Metric Completion of Regular Rings.

Walter D. Burgess, David E. Handelman (1982)

Mathematische Annalen

The representation dimension of domestic weakly symmetric algebras

Rafał Bocian, Thorsten Holm, Andrzej Skowroński (2004)

Open Mathematics

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras...

The Ziegler spectrum of a tame hereditary algebra

Claus Ringel (1998)

Colloquium Mathematicae

Torsion free types

John Dauns (1991)

Fundamenta Mathematicae

Über absolut reine Ringe.

Tilmann Würfel (1973)

Journal für die reine und angewandte Mathematik

Unzerlegbare, injektive Moduln über Kettenringen.

Günter Törner (1976)

Journal für die reine und angewandte Mathematik

VNR rings, $Π$ -regular rings and annihilators

Roger Yue Chi Ming (2009)

Commentationes Mathematicae Universitatis Carolinae

Von Neumann regular rings, hereditary rings, semi-simple Artinian rings, self-injective regular rings are characterized. Rings which are either strongly regular or semi-simple Artinian are considered. Annihilator ideals and $Π$ -regular rings are studied. Properties of WGP-injectivity are developed.

Weak baer modules localized with respect to a torsion theory

Seog Hoon Rim, Mark L. Teply (1998)

Czechoslovak Mathematical Journal

Weak $n$ -injective and weak $n$ -fat modules

Umamaheswaran Arunachalam, Saravanan Raja, Selvaraj Chelliah, Joseph Kennedy Annadevasahaya Mani (2022)

Czechoslovak Mathematical Journal

We introduce and study the concepts of weak $n$ -injective and weak $n$ -flat modules in terms of super finitely presented modules whose projective dimension is at most $n$ , which generalize the $n$ -FP-injective and $n$ -flat modules. We show that the class of all weak $n$ -injective $R$ -modules is injectively resolving, whereas that of weak $n$ -flat right $R$ -modules is projectively resolving and the class of weak $n$ -injective (or weak $n$ -flat) modules together with its left (or right) orthogonal class forms a hereditary...

Currently displaying 201 – 220 of 242

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Displaying 201 – 220 of 242

The component quiver of a self-injective artin algebra

The existence of envelopes

The existence of relative pure injective envelopes

The flat dimensions of injective modules.

The general structure of inverse polynomial modules

The importance of rational extensions

The N*-Metric Completion of Regular Rings.

The representation dimension of domestic weakly symmetric algebras

The Ziegler spectrum of a tame hereditary algebra

Torsion free types

Über absolut reine Ringe.

Unzerlegbare, injektive Moduln über Kettenringen.

VNR rings, $Π$ -regular rings and annihilators

Weak baer modules localized with respect to a torsion theory

Weak $n$ -injective and weak $n$ -fat modules

Алгебры Хопфа с инволюцией над некоммутативными кольцами и их гомологии. I

Еще о квазифробениусовых кольцах

Индуктивно замкнутые собственные классы над ограниченными hnp-кольцами.

Инъективные минимальные модули

К понятию инъективности в категории модулей

Currently displaying 201 – 220 of 242