A characterization of minimal prime ideals
1998 ◽
Vol 40
(2)
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pp. 223-236
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Keyword(s):
AbstractLet P be a prime ideal of a ring R, O(P) = {a ∊ R | aRs = 0, for some s ∊ R/P} | and Ō(P) = {x ∊ R | xn ∊ O(P), for some positive integer n}. Several authors have obtained sheaf representations of rings whose stalks are of the form R/O(P). Also in a commutative ring a minimal prime ideal has been characterized as a prime ideal P such that P= Ō(P). In this paper we derive various conditions which ensure that a prime ideal P = Ō(P). The property that P = Ō(P) is then used to obtain conditions which determine when R/O(P) has a unique minimal prime ideal. Various generalizations of O(P) and Ō(P) are considered. Examples are provided to illustrate and delimit our results.
Keyword(s):
2019 ◽
Vol 19
(10)
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pp. 2050199
Keyword(s):
1983 ◽
Vol 35
(2)
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pp. 194-196
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2019 ◽
Vol 18
(07)
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pp. 1950123
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Keyword(s):
1971 ◽
Vol 23
(5)
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pp. 749-758
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Keyword(s):
2000 ◽
Vol 43
(3)
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pp. 312-319
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1965 ◽
Vol 115
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pp. 110-110
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