Prime Ideals in Regular Self-Injective Rings
1973 ◽
Vol 25
(4)
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pp. 829-839
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Although the notion of the maximal quotient ring of a nonsingular ring has been around for some time, not much is known about its structure in general beyond the important theorems of Johnson and Utumi [4; 11] that it is von Neumann regular and self-injective. The purpose of this paper is to study the structure of such a regular, self-injective ring R by looking at its prime ideals. Initially, we show that the primes of R separate into two types, called ‘'essential” and ‘“closed”, and that for any prime P, the two-sided ideals in the ring R/P are linearly ordered.
1972 ◽
Vol 15
(2)
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pp. 301-303
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1972 ◽
Vol 24
(5)
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pp. 835-850
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2011 ◽
Vol 2011
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pp. 1-9
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2011 ◽
Vol 10
(06)
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pp. 1351-1362
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1977 ◽
Vol 20
(2)
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pp. 263-265
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2015 ◽
Vol 14
(05)
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pp. 1550061
1988 ◽
Vol 102
(3)
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pp. 480-480
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2018 ◽
Vol 55
(2)
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pp. 270-279
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2009 ◽
Vol 08
(05)
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pp. 601-615
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