S-∗w-Principal Ideal Domains
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Let D be an integral domain, ∗ a star-operation on D, and S a multiplicative subset of D. We define D to be an S-∗w-principal ideal domain if for each nonzero ideal I of D, there exist an element s ∈ S and a principal ideal (c) of D such that [Formula: see text]. In this paper, we study some properties of S-∗w-principal ideal domains. Among other things, we study the local property, the Nagata type theorem, and the Cohen type theorem for S-∗w-principal ideal domains.
1986 ◽
Vol 29
(1)
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pp. 25-32
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2004 ◽
Vol 23
(4)
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pp. 114-125
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1971 ◽
Vol 5
(1)
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pp. 87-94
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1991 ◽
Vol 157
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pp. 141-145
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1969 ◽
Vol 10
(3-4)
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pp. 395-402
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