Let G be a finite group and k be a field of characteristic p. The connection between the modular representations and the cohomology of G has been a subject of major interest over the last several years. For example, recent study of the stable category of kG-modules StMod(kG) led Rickard [27] to introduce certain idempotent modules and functors. This has led to a theory of varieties for infinite...

We will develop the model theory of modules over commutative Bézout domains. In particular we characterize commutative Bézout domains B whose lattice of pp-formulae has no width and give some applications to the existence of superdecomposable pure injective

We investigate width and Krull–Gabriel dimension over commutative Noetherian rings which are “tame” according to the Klingler–Levy analysis in [4], [5] and [6], in particular over Dedekind-like rings and their homomorphic images. We show that both are undefined in most cases.

For a ring R, call a class C of R-modules (pure-) mono-correct if for any M,N ∈ C the existence of (pure) monomorphisms M → N and N → M implies M ' N . Extending results and ideas of Rososhek from rings to modules, it is shown that, for an R-module M , the class σ[M ] of all M -subgenerated modules is mono-correct if and only if M is semisimple, and the class of all weakly M -injective modules ...

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A linear deformation of a Meyer set M in R is the image of M under a group homomorphism of the group [M ] generated by M into R. We provide a necessary and sufficient condition for such a deformation to be a Meyer set. In the case that the deformation is a Meyer set and the deformation is injective, the deformation is pure point diffractive if the orginal set M is pure point diffractive. AMS Cl...

‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...