Continuous Rings and Rings of Quotients
1978 ◽
Vol 21
(3)
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pp. 319-324
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Keyword(s):
Throughout R will denote an associative ring with identity. Let Zℓ(R) be the left singular ideal of R. It is well known that Zℓ(R) = 0 if and only if the left maximal ring of quotients of R, Q(R), is Von Neumann regular. When Zℓ(R) = 0, q(R) is also a left self injective ring and is, in fact, the injective hull of R. A natural generalization of the notion of injective is the concept of left continuous as studied by Utumi [4]. One of the major obstacles to studying the relationships between Q(R) and R is a description of J(Q(R)), the Jacobson radical of Q(R). When a ring is left continuous, then its left singular ideal is its Jacobson radical. This facilitates the study of the cases when either Q(R) is continuous or R is continuous.
2009 ◽
Vol 08
(05)
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pp. 601-615
Keyword(s):
1975 ◽
Vol 18
(2)
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pp. 233-239
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Keyword(s):
2013 ◽
Vol 12
(07)
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pp. 1350025
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1964 ◽
Vol 7
(3)
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pp. 405-413
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Keyword(s):
1980 ◽
Vol 23
(2)
◽
pp. 173-178
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Keyword(s):
1972 ◽
Vol 15
(2)
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pp. 301-303
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1969 ◽
Vol 21
◽
pp. 865-875
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Keyword(s):
Keyword(s):
1968 ◽
Vol 68
(1)
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pp. 30-53
Keyword(s):
Keyword(s):