Skew polynomial rings over σ-skew Armendariz rings

• Main Authors: V.K. Bhat, Meeru Abrol
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2016-12-01
• Series: Cogent Mathematics
• Subjects: Noetherian ring; Armendariz rings; endomorphism; 2-primal ring
• Online Access: http://dx.doi.org/10.1080/23311835.2016.1183287

This article concerns skew polynomial rings over Armendariz rings and $ \sigma $-skew Armendariz ring. Let R be a Noetherian, Armendariz, prime ring. In this paper we prove that R and the polynomial ring R[x] are 2-primal. Further we prove that if $ \sigma $ is an endomorphism of a ring R, then (1) R is a $ \sigma $-skew Armendariz ring implies that $ R[x;\sigma ] $ is a $ \overline{\sigma } $-skew Armendariz ring, where $ \overline{\sigma } $ is an extension of $ \sigma $ to $ R[x;\sigma ] $. (2) R is a $ \sigma $-rigid implies that $ R[x;\sigma ] $ is a 2-primal.