Protective modules over polynomial rings over division rings

Modules over Differential Polynomial Rings

This note announces a number of results on the structure of differential modules over differential rings, where differential ring means a ring with a family of derivations and differential module means a module having a family of operators compatible with the derivations of the ring. To fix notation, throughout the paper we let A denote an associative ring, M = AM an 4-module, k the correspondi...

On nest modules of matrices over division rings

Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...

Triangulaizability of Algebras Over Division Rings

Codes as Modules over Skew Polynomial Rings

In previous works we considered codes defined as ideals of quotients of non commutative polynomial rings, so called Ore rings of automorphism type. In this paper we consider codes defined as modules over non commutative polynomial rings, removing therefore some of the constraints on the length of the codes defined as ideals. The notion of BCH codes can be extended to this new approach and the c...

Projecttve Modules over Laurent Polynomial Rings

Quillen's solution of Serre's problem is extended to Laurent polynomial rings. An example is given of a A[T, r~']-module P which is not extended even though A is regular and Pm is extended for all maximal ideals m of A. The object of this note is to present several comments and examples related to some problems suggested by Quillen's recent solution of Serre's problem [7]. It is an immediate co...