Overrings of the Kronecker function ring Kr(D, *) of a Prüfer *-multiplication domain D
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Let * be an e.a.b. star operation on an integrally closed domain D, and let Kr(D,*) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping Dα ↦ Kr(Dα, v) is a bijection from the set {Dα} of *-linked overrings of D into the set of overrings of Kr(D, v). This is a generalization of [5, Proposition 32.19] that if D is a Prüfer domain, then the mapping Dα↦ Kr(Dα, b) is a one-to-one mapping from the set {Dα} of overrings of D onto the set of overrings of Kr(D, b).
Abstract
Let * be an e.a.b. star operation on an integrally closed domain D, and let Kr(D,*) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping Dα ↦ Kr(Dα, v) is a bijection from the set {Dα} of *-linked overrings of D into the set of overrings of Kr(D, v). This is a generalization of [5, Proposition 32.19] that if D is a Prüfer domain, then the mapping Dα↦ Kr(Dα, b) is a one-to-one mapping from the set {Dα} of overrings of D onto the set of overrings of Kr(D, b).
참고문헌 (6)
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