A Decomposition of Rings Generated by Faithful Cyclic Modules
1989 ◽
Vol 32
(3)
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pp. 333-339
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Keyword(s):
AbstractA ring R is said to be generated by faithful right cyclics (right finitely pseudo-Frobenius), denoted by GFC (FPF), if every faithful cyclic (finitely generated) right R-module generates the category of right R-modules. The class of right GFC rings includes right FPF rings, commutative rings (thus every ring has a GFC subring - its center), strongly regular rings, and continuous regular rings of bounded index. Our main results are: (1) a decomposition of a semi-prime quasi-Baer right GFC ring (e.g., a semiprime right FPF ring) is achieved by considering the set of nilpotent elements and the centrality of idempotnents; (2) a generalization of S. Page's decomposition theorem for a right FPF ring.
1971 ◽
Vol 4
(1)
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pp. 57-62
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Keyword(s):
2009 ◽
Vol 08
(05)
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pp. 601-615
Keyword(s):
2019 ◽
Vol 18
(02)
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pp. 1950035
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2013 ◽
Vol 24
(2)
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Keyword(s):
Keyword(s):
1983 ◽
Vol 6
(1)
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pp. 119-124
2017 ◽
Vol 16
(10)
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pp. 1750187
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Keyword(s):
1973 ◽
Vol 38
(2)
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pp. 381-381
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