In this paper we generalize a result of Urban on the structure of residually reducible representations on local Artinian rings from the case that the semi-simplification of the residual representation splits into 2 absolutely irreducible representations to the case where it splits into m ≥ 2 absolutely irreducible representations.

Picard-Vessiot rings are present in many settings like differential Galois theory, difference Galois theory and Galois theory of Artinian simple module algebras. In this article we set up an abstract framework in which we can prove theorems on existence and uniqueness of Picard-Vessiot rings, as well as on Galois groups corresponding to the Picard-Vessiot rings. As the present approach restrict...

Meta-projective modules on a ring R were essentially studied by Feng Lianggui and Tong Wenting in [3] when R is a commutative ring. While Duo-rings were studied by A. L. Fall in [2] and by M. Sanghare in [8]. The results of [3] were extended by M. O. Abdelkader in [5] to the duo-ring case by providing characterizations of Duo-rings. In this note, we give an extension of the MP-dimension notion ...

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.