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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.
In this paper we compute injective, projective and flat dimensions of inverse polynomial modules as -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 rational completion of an -module can be characterized as a -injective hull of with respect to a (hereditary) torsion functor depending on . Properties of a torsion functor depending on an -module are studied.
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.
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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