On inverse skew Laurent series extensions of weakly rigid rings |
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Authors: | Mohammad Habibi |
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Institution: | 1. Department of Mathematics, University of Tafresh, Tafresh, Iranmhabibi@tafreshu.ac.ir habibi.mohammad2@gmail.com |
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Abstract: | Let R be a ring equipped with an automorphism α and an α-derivation δ. We studied on the relationship between the quasi Baerness and (α, δ)-quasi Baerness of a ring R and these of the inverse skew Laurent series ring R((x?1; α, δ)), in case R is an (α, δ)-weakly rigid ring. Also we proved that for a semicommutative (α, δ)-weakly rigid ring R, R is Baer if and only if so is R((x?1; α, δ)). Moreover for an (α, δ)-weakly rigid ring R, it is shown that the inverse skew Laurent series ring R((x?1; α, δ)) is left p.q.-Baer if and only if R is left p.q.-Baer and every countable subset of left semicentral idempotents of R has a generalized countable join in R. |
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Keywords: | Inverse skew Laurent series ring principally quasi Baer ring (α δ)-quasi Baer ring quasi Baer ring weakly rigid ring |
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