Covering classes and uniserial modules

Almost uniserial modules

An R-module M is called Almost uniserial module, if any two non-isomorphic submodules of M are linearly ordered by inclusion. In this paper, we investigate some properties of Almost uniserial modules. We show that every finitely generated Almost uniserial module over a Noetherian ring, is torsion or torsionfree. Also the construction of a torsion Almost uniserial modules whose first nonzero Fit...

Explicitly Non-Standard Uniserial Modules

A new construction is given of non-standard uniserial modules over certain valuation domains; the construction resembles that of a special Aronszajn tree in set theory. A consequence is the proof of a sufficient condition for the existence of non-standard uniserial modules; this is a theorem of ZFC which complements an earlier independence result.

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

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.