The Cohen Type Theorem for S-*w-Principal Ideal Domains

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doi:http://dx.doi.org/10.7858/eamj.2018.036

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The Cohen Type Theorem for S-*w-Principal Ideal Domains

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S-∗w-principal ideal domain Cohen type theorem.

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초록

Let D be an integral domain, ∗ a star-operation on D, and S a (not necessarily saturated) multiplicative subset of D. In this article, we prove the Cohen type theorem for S-∗w-principal ideal domains, which states that D is an S-∗w-principal ideal domain if and only if every nonzero prime ideal of D (disjoint from S) is S-∗w-principal.

Abstract

Let D be an integral domain, ∗ a star-operation on D, and S a (not necessarily saturated) multiplicative subset of D. In this article, we prove the Cohen type theorem for S-∗w-principal ideal domains, which states that D is an S-∗w-principal ideal domain if and only if every nonzero prime ideal of D (disjoint from S) is S-∗w-principal.

참고문헌 (5)

D.D. Anderson, "S-Noetherian rings", Comm. Algebra, 30, pp.4407~4416 (2002)[DOI]
B.G. Kang, "On the converse of a well-known fact about Krull domains", J. Algebra, 124, pp.284~299 (1989)[DOI]
I. Kaplansky, "Commutative Rings" (1994), Polygonal Publishing House
H. Kim, "On S-strong Mori domains", J. Algebra, 416, pp.314~332 (2014)[DOI]
H. Kim, "On S-<TEX>$*_w$<", TEX>-principal ideal domains, 2018, pp.25, 217~224

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Abstract

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