The Some Properties of Skew Polynomial Rings - Chu, Qianqian; Jin, Hailan (Scientific Research Publishing, 2016)
This paper mainly studies some properties of skew polynomial ring related to Morita invariance, Armendariz and (quasi)-Baer. First, we show that skew polynomial ring has no Morita invariance by the counterexample. Then we prove a necessary condition that skew polynomial ring constitutes Armendariz ring. We lastly investigate that condition of skew polynomial ring is a (quasi)-Baer ring, and verify that the conditions is necessary, but not sufficient by example and counterexample.
Keywords: Skew Polynomial Ring; (Quasi)-Baer Ring; Armendariz Ring; Morita Context Ring; Morita Invariance; Nozero Divisor Ring