On inverse skew Laurent series extensions of weakly rigid rings

Abstract

Let $R$ be a ring equipped with an automorphism $alpha$ and an $alpha$-derivation $delta$. We studied on the relationship between the quasi Baerness and $(alpha,delta)$-quasi Baerness of a ring $R$ and these of the inverse skew Laurent series ring $R((x^{-1};alpha,delta))$, in case $R$ is an $(alpha,delta)$-weakly rigid ring. Also we proved that for a semicommutative $(alpha,delta)$-weakly rigid ring $R$, $R$ is Baer if and only if so is $R((x^{-1};alpha,delta))$. Moreover for an $(alpha,delta)$-weakly rigid ring $R$, it is shown that the inverse skew Laurent series ring $R((x^{-1};alpha,delta))$ 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 $R$.