Skew Polynomial Ring of the Ring of Morita Context

Abstract

Ghahramani proved that the skew polynomial ring of the formal triangular matrix ring is isomorphic to a formal triangular matrix ring. We aim to generalize this work to the skew polynomial ring of a ring of Morita context. Let M be a ring of Morita context and M[z; θ, d] be a skew polynomial ring over M. By studying a particular ring homomorphism θ and a skew derivation d on M, one can show that M[z; θ, d] is isomorphic to a ring of Morita context that is constructed by skew polynomial modules and skew polynomial rings. In this article, we use the definition of skew polynomial module that was introduced in the work of Ghahramani.

Key words and phrases. Homomorphism, ring of Morita context, skew derivation, skew polynomial rings.

2020 Mathematics Subject Classification. 16S36; 16G99