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OVERRINGS OF THE KRONECKER FUNCTION RING Kr(D, *) OF A PRUFER *-MULTIPLICATION DOMAIN D

  • Published : 2009.09.30

Abstract

Let * be an e.a.b. star operation on an integrally closed domain D, and let $K\gamma$(D, *) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping $D_{\alpha}{\mapsto}K{\gamma}(D_{\alpha},\;{\upsilon})$ is a bijection from the set {$D_{\alpha}$} of *-linked overrings of D into the set of overrings of $K{\gamma}(D,\;{\upsilon})$. This is a generalization of [5, Proposition 32.19] that if D is a Pr$\ddot{u}$fer domain, then the mapping $D_{\alpha}{\mapsto}K_{\gamma}(D_{\alpha},\;b)$ is a one-to-one mapping from the set {$D_{\alpha}$} of overrings of D onto the set of overrings of $K_{\gamma}$(D, b).

Keywords

References

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  2. THE KRONECKER FUNCTION RING OF THE RING D[X]N* vol.47, pp.5, 2010, https://doi.org/10.4134/BKMS.2010.47.5.907