THE COHN-JORDAN EXTENSION AND SKEW MONOID RINGS OVER A QUASI-BAER RING

Title & Authors
THE COHN-JORDAN EXTENSION AND SKEW MONOID RINGS OVER A QUASI-BAER RING
HASHEMI EBRAHIM;

Abstract
A ring R is called (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 $\small{\beta}$ and R be G-compatible. It is shown that R is (left principally) quasi-Baer if and only if skew monoid ring $\small{R_{\beta}[G]}$ 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 $\small{A(R,\;\beta)}$ is (left principally) quasi-Baer if and only if left Ore quotient ring $\small{G^{-1}R_{\beta}[G]}$ is (left principally) quasi-Baer.
Keywords
quasi-Baer rings;left principally quasi-Baer rings;compatible rings;skew monoid rings;Cohn-Jordan extension;skew Laurent extension;Ore quotient rings;
Language
English
Cited by
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2.
Left principally quasi-Baer and left APP-rings of skew generalized power series, Journal of Algebra and Its Applications, 2015, 14, 03, 1550038
3.
ON ANNIHILATOR IDEALS OF SKEW MONOID RINGS, Glasgow Mathematical Journal, 2010, 52, 01, 161
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