On two-sided artinian quotient rings
1972 ◽
Vol 13
(2)
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pp. 159-163
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Keyword(s):
Djabali [1] has proved that, if R is a right and left noetherian ring with an identity and if the proper prime ideals of R are maximal, then R has a right and left artinian two-sided quotient ring. Robson [5, Theorem 2.11] and Small [6, Theorem 2.13] have proved independently that, if Ris a commutative noetherian ring, then Rhas an artinian quotient ring if and only if the prime ideals of Rthat belong to the zero ideal are all minimal. We shall generalise these results by proving theTheorem. Let R be a right and left noetherian ring with a regular element. Then R has a right and left artinian two-sided quotient ring if and only if each prime ideal of R consisting of zero–divisors is minimal.
1988 ◽
Vol 53
(1)
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pp. 284-293
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Keyword(s):
1979 ◽
Vol 20
(2)
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pp. 125-128
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Keyword(s):
1972 ◽
Vol 24
(4)
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pp. 703-712
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1991 ◽
Vol 34
(1)
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pp. 155-160
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1977 ◽
Vol 29
(5)
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pp. 914-927
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Keyword(s):
2016 ◽
Vol 15
(05)
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pp. 1650088
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Keyword(s):