Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 389–395

Skew inverse power series rings over a ring with projective socle

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Abstract

A ring R is called a right PS-ring if its socle, Soc(RR), is projective. Nicholson and Watters have shown that if R is a right PS-ring, then so are the polynomial ring R[x] and power series ring R[[x]]. In this paper, it is proved that, under suitable conditions, if R has a (flat) projective socle, then so does the skew inverse power series ring R[[x−1; α, δ]] and the skew polynomial ring R[x; α, δ], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Our results extend and unify many existing results. Examples to illustrate and delimit the theory are provided.

Keywords

skew inverse power series ring skew polynomial ring annihilator projective socle ring flat socle ring 

MSC 2010

16W60 16W70 16S36 16P40 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of Basic Sciences, Garmsār BranchIslamic Azad UniversityGarmsārIran

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