On pure-injective modules over pullback rings

Let R be the pullback, in the sense of [9], of two Dedekind domains. We describe all those indecomposable pure-injective R-modules M with finite-dimensional top, that is, such that M/Rad(R)M is finite dimensional over R/Rad(R).     

Endomorphism rings of some Young modules

Let \({\Sigma_r}\) be the symmetric group acting on \({r}\) letters, \({K}\) be a field of characteristic 2, and \({\lambda}\) and \({\mu}\) be partitions of \({r}\) in at most two parts. Denote the permutation module corresponding to the Young subgroup \({\Sigma_\lambda}\), in \({\Sigma_r}\), by \({M^\lambda}\), and the indecomposable Young module by \({Y^\mu}\). We give an explicit presentation of the endomorphism algebra \({{\rm End}_{k[\Sigma_r]}(Y^\mu)}\) using the idempotents found by Doty et al. (J Algebra 307(1):377–396, 2007).     

Endomorphism rings of simple modules over group rings

If is a finitely generated nilpotent group which is not abelian-by-finite, a field, and a finite dimensional separable division algebra over , then there exists a simple module for the group ring with endomorphism ring . An example is given to show that this cannot be extended to polycyclic groups.

     

Endomorphism rings of modules and lattices of submodules

This survey covers material inReferativnyi Zhurnal Matematika and is a continuation of A. V. Mikhalev's survey in Algebra. Topology. Geometry, Vol. 12 (Itogi Nauki i Tekhniki (1974)). Papers on endomorphism rings of modules over associative rings and on lattices of submodules are considered.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 21, pp. 183–254, 1983.     

Endomorphism rings and automorphism groups of almost completely decomposable groups

To every non-cuspidal K-rational point on the modular curve X_l(n) a non-commutative Noetherian domain of global dimension 3 can be associated : the Sklyanin algebra. In this paper we give the defining equations of the Sklyanin algebras and their centers when X_l(n) is rational, i.e. n <= 10 or n = 12.     

Endomorphism rings and the category of finitely generated projective modules

Given a left R-module M, we study the connection between the (right and left) properties of its endomorphism ring S=End(_RM) and the properties of the category σ _f [M] of all submodules of finitely M-generated left R-modules.     

Cotilting modules are pure-injective

We prove that a cotilting module over an arbitrary ring is pure-injective.