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

Title & Authors
OVERRINGS OF THE KRONECKER FUNCTION RING Kr(D, *) OF A PRUFER *-MULTIPLICATION DOMAIN D
Chang, Gyu-Whan;

Abstract
Let * be an e.a.b. star operation on an integrally closed domain D, and let $\small{K\gamma}$(D, *) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping $\small{D_{\alpha}{\mapsto}K{\gamma}(D_{\alpha},\;{\upsilon})}$ is a bijection from the set {$\small{D_{\alpha}}$} of *-linked overrings of D into the set of overrings of $\small{K{\gamma}(D,\;{\upsilon})}$. This is a generalization of [5, Proposition 32.19] that if D is a Pr$\small{\ddot{u}}$fer domain, then the mapping $\small{D_{\alpha}{\mapsto}K_{\gamma}(D_{\alpha},\;b)}$ is a one-to-one mapping from the set {$\small{D_{\alpha}}$} of overrings of D onto the set of overrings of $\small{K_{\gamma}}$(D, b).
Keywords
star operation;Pr$\small{\ddot{u}}$ *-multiplication domain;Kronecker functionring;*-linked overring;
Language
English
Cited by
1.
THE KRONECKER FUNCTION RING OF THE RING D[X]N*,;

대한수학회보, 2010. vol.47. 5, pp.907-913
2.
FINITELY t-VALUATIVE DOMAINS,;

Korean Journal of Mathematics, 2014. vol.22. 4, pp.591-598
1.
FINITELY t-VALUATIVE DOMAINS, Korean Journal of Mathematics, 2014, 22, 4, 591
2.
THE KRONECKER FUNCTION RING OF THE RING D[X]N*, Bulletin of the Korean Mathematical Society, 2010, 47, 5, 907
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