Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of x − λ, where λ is a unit element, are exhibited. When λ = 1, the generators of Euclidean and Hermitian dual codes of such codes are determined tog...

where 7-[ is the category of finitely presented E-torsion R-modules of projective dimension 1. An explicit construction for 0 is given, generalizing that previously worked out by Bass when ~ is central. Application is made to work of Farrell and Hsiang on skew polynomial tings, and to the Whitehead groups of those division rings that occur as fields of fractions ofnoncommutative Euclidean domains.

We introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. We firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. We next argue about the strong$alpha$-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown ...