Let R be an associative ring. This monograph deals with the right R-modules MR whose
endomorphism ring End (MR) is semilocal. More generally, let A be any preadditive …

Let H be a Krull monoid with infinite cyclic class group G and let GP⊂ G denote the set of
classes containing prime divisors. We study under which conditions on GP some of the main …

A module M is called automorphism-invariant if it is invariant under automorphisms of its
injective envelope. In this paper, we study the endomorphism rings of automorphism …

It is proved that two diagonal matrices diag (a1,…, an) and diag (b1,…, bn) over a local ring
R are equivalent if and only if there are two permutations σ, τ of {1, 2,…, n} such that …

According to the classical Krull–Schmidt Theorem, any module of finite composition length
decomposes as a direct sum of indecomposable modules in an essentially unique way, that …

We show that the endomorphism rings of kernels ker ϕ of non-injective morphisms ϕ
between indecomposable injective modules are either local or have two maximal ideals, the …

We show that the indecomposable R-modules whose endomorphism ring has finitely many
maximal right ideals, all of them two-sided, have a surprisingly simple behavior as far as …

We prove that for a noetherian semilocal ring R with exactly k isomorphism classes of simple
right modules the monoid V*(R) of isomorphism classes of countably generated projective …

The aim of this paper is to embed additive categories in which direct-sum decompositions
into indecomposables are not unique but have a regular geometric behavior into categories …

A module UR is couniform if it has dual Goldie dimension 1, that is, it is non-zero and the
sum of any two proper submodules of UR is a proper submodule of UR. A module MR is …