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ON ANNIHILATOR IDEALS OF SKEW MONOID RINGS*

Published online by Cambridge University Press:  04 December 2009

LIU ZHONGKUI  and
YANG XIAOYAN
LIU ZHONGKUI
Affiliation:
Department of Mathematics, Northwest Normal University Lanzhou 730070, Gansu, People's Republic of China e-mail: liuzk@nwnu.edu.cn
YANG XIAOYAN
Affiliation:
Department of Mathematics, Northwest Normal University Lanzhou 730070, Gansu, People's Republic of China e-mail: liuzk@nwnu.edu.cn
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Abstract

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A ring R is called a left APP-ring if the left annihilator lR(Ra) is pure as a left ideal of R for every a ∈ R; 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 and M an ordered monoid. Assume that there is a monoid homomorphism φ: M ⟶ Aut(R). We give a necessary and sufficient condition for the skew monoid ring (induced by φ) to be left APP (left principally quasi-Baer, quasi-Baer, respectively).

Keywords

16S3516S36
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 1 , January 2010 , pp. 161 - 168
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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