On (von Neumann) regular rings
1974 ◽
Vol 19
(1)
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pp. 89-91
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Keyword(s):
Throughout, A denotes an associative ring with identity and “module” means “left, unitary A-module”. In (3), it is proved that A is semi-simple, Artinian if A is a semi-prime ring such that every left ideal is a left annihilator. A natural question is whether a similar result holds for a (von Neumann) regular ring. The first proposition of this short note is that if A contains no non-zero nilpotent element, then A is regular iff every principal left ideal is the left annihilator of an element of A. It is well-known that a commutative ring is regular iff every simple module is injective (I. Kaplansky, see (2, p. 130)). The second proposition here is a partial generalisation of that result.
1969 ◽
Vol 12
(4)
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pp. 417-426
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Keyword(s):
1974 ◽
Vol 17
(2)
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pp. 283-284
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Keyword(s):
2006 ◽
Vol 2006
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pp. 1-6
Keyword(s):
1982 ◽
Vol 25
(1)
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pp. 118-118
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Keyword(s):
1995 ◽
Vol 51
(3)
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pp. 433-437
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Keyword(s):
2018 ◽
Vol 17
(04)
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pp. 1850075
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Keyword(s):
2009 ◽
Vol 08
(05)
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pp. 601-615
Keyword(s):