Decomposition of modules over right uniserial rings

ω1-generated uniserial modules over chain rings

The purpose of this paper is to provide a criterion of an occurrence of uncountably generated uniserial modules over chain rings. As we show it suffices to investigate two extreme cases, nearly simple chain rings, i.e. chain rings containing only three twosided ideals, and chain rings with “many” two-sided ideals. We prove that there exists an ω1-generated uniserial module over every non-artini...

Divisible Uniserial Modules over Valuation Domains

Associated Graphs of Modules Over Commutative Rings

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...

SOME REMARKS ON ALMOST UNISERIAL RINGS AND MODULES

In this paper we study almost uniserial rings and modules. An R−module M is called almost uniserial if any two nonisomorphic submodules are linearly ordered by inclusion. A ring R is an almost left uniserial ring if R_R is almost uniserial. We give some necessary and sufficient condition for an Artinian ring to be almost left uniserial.

Pure-injective Modules over Right Noetherian Serial Rings

We give a criterion for the existence of a super-decomposable pure-injective module over an arbitrary serial ring.