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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 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 M ¯ of an R -module M can be characterized as a τ M -injective hull of M with respect to a (hereditary) torsion functor τ M depending on M . Properties of a torsion functor depending on an R -module M are studied.

The irreducible components of the nilpotent associative algebras.

Abdenacer Makhlouf (1993)

Revista Matemática de la Universidad Complutense de Madrid

The aim of this work is to describe the irreducible components of the nilpotent complex associative algebras varieties of dimension 2 to 5 and to give a lower bound of the number of these components in any dimension.

The periodicity conjecture for blocks of group algebras

Karin Erdmann, Andrzej Skowroński (2015)

Colloquium Mathematicae

We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.

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