The Cohn-Jordan extension and skew monoid rings over a quasi-Baer ring

Commun. Korean Math. Soc. 2006 Vol. 21, No. 1, 1-9 Printed March 1, 2006

Ebrahim Hashemi Shahrood University of Technology

Abstract : A ring $R$ is called (\emph{left principally) quasi-Baer} if the left annihilator of every (principal) left ideal of $R$ is generated by an idempotent. Let $R$ be a ring, $G$ be an ordered monoid acting on $R$ by $\beta$ and $R$ be $G$-compatible. It is shown that $R$ is (left principally) quasi-Baer if and only if skew monoid ring $R_{\beta}[G]$ is (left principally) quasi-Baer. If $G$ is an abelian monoid, then $R$ is (left principally) quasi-Baer if and only if the Cohn-Jordan extension $A(R,\beta)$ is (left principally) quasi-Baer if and only if left Ore quotient ring $G^{-1}R_{\beta}[G]$ is (left principally) quasi-Baer.