We study the category Morph (Mod-R) whose objects are all morphisms between two right R-
modules. The behavior of the objects of Mod-R whose endomorphism ring in Morph (Mod-R) …

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 …

The well-known Krull–Schmidt–Azumaya theorem gives sufficient conditions for a module to
have an essentially unique decomposition as a direct sum of indecomposable submodules …

The aim of this paper is to study the modules M with a finite direct sum decomposition M= M
1⊕…⊕ Mn such that all the endomorphism rings End (Mi) are homogeneous semilocal. In …

Let R be a ring and C a class of right R-modules closed under finite direct sums. If we
suppose that C has a set of representatives, that is, a set V (C)⊆ C such that every M∈ C is …

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to
and irreducible epimorphisms from finitely generated free modules over a noetherian local …

The paper is a study of modules with a local endomorphism ring. We consider
decompositions of modules and give a simple proof of Azumaya's theorem. We also define …

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 R be a local ring order, ie a one-dimensional local (noetherian) ring whose completion R
is reduced, and let M be a finitely generated R-module. We consider two monoids:+(M) …

Direct summands of products Page 1 0003-889X/02/010012-12 $ 3.90/0 Arch. Math. 78 (2002)
12–23 Sonderdruck aus © Birkhäuser Verlag, Basel, 2002 Direct summands of products By LIDIA …