Quasi-Baer and biregular generalized matrix rings
2017 ◽
Vol 16
(04)
◽
pp. 1750067
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Keyword(s):
Generalized matrix rings are ubiquitous in algebra and have relevant applications to analysis. A ring is quasi-Baer (respectively, right p.q.-Baer) in case the right annihilator of any ideal (respectively, principal ideal) is generated by an idempotent. A ring is called biregular if every principal ideal is generated by a central idempotent. In this paper, we identify the ideals and principal ideals, the annihilators of ideals, and the central and semi-central idempotents of a generalized [Formula: see text] matrix ring. We characterize the generalized matrix rings that are quasi-Baer, right p.q.-Baer, prime, and biregular. We provide examples to illustrate these concepts.
2010 ◽
Vol 53
(4)
◽
pp. 587-601
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Keyword(s):
1995 ◽
Vol 18
(2)
◽
pp. 311-316
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Keyword(s):
2016 ◽
Vol 15
(07)
◽
pp. 1650121
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2019 ◽
Vol 19
(01)
◽
pp. 2050018
Keyword(s):
2018 ◽
Vol 17
(02)
◽
pp. 1850029
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Keyword(s):
1979 ◽
Vol 20
(2)
◽
pp. 125-128
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Keyword(s):
1995 ◽
Vol 38
(2)
◽
pp. 174-176
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Keyword(s):