On Skew Armendariz of Laurent Series Type Rings

摘要

Let α be an automorphism of a ring R. We study the skew Armendariz of Laurent series type rings (α-LA rings), as a generalization of the standard Armendariz condition from polynomials to skew Laurent series. We study on the relationship between the Baerness and p.p. property of a ring R and these of the skew Laurent series ring R[[x, x −1; α]], in case R is an α-LA ring. Moreover, we prove that for an α-weakly rigid ring R, R[[x, x −1; α]] is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of S _ℓ(R) has a generalized countable join in R. Various types of examples of α-LA rings are provided.View full textDownload full textKey WordsArmendariz rings, Skew Laurent series rings, Baer rings, Weakly rigid rings2000 Mathematics Subject ClassificationPrimary 16A05, Secondary 16N40Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927872.2011.600746