Prufer *-multiplication domains, Nagata rings, and Kronecker function rings

JOURNAL OF ALGEBRA

卷:319

Article

Chang, Gyu Whan

关键词: (e.a.b.) *-operation;    Prufer *-multiplication domain;    Nagata ring;    Kronecker function ring;   

DOI  :  10.1016/j.jalgebra.2007.10.010

来源: Elsevier

【 摘 要 】

Let D be an integrally closed domain, * a star-operation on D, X an indeterminate over D, and N*= {f is an element of D[X] | (A(f))* = D}. For an e.a.b. star-operation *(1) on D, let Kr(D, *(1)) be the Kronecker function ring of D with respect to *(1). In this paper, we use * to define a new e.a.b. star-operation *(c) on D. Then we prove that D is a Prufer *-multiplication domain if and only if D[X](N*) = Kr(D, *(c)), if and only if Kr(D, *(c)) is a quotient ring of D[X], if and only if Kr(D, *(c)) is a flat D[X]-module, if and only if each *-linked overring of D is a Prufer v-multiplication domain. This is a generalization of the following well-known fact that if D is a v-domain, then D is a Pruter v-multiplication domain if and only if Kr(D, v) = D[X]N-v, if and only if Kr(D, v) is a quotient ring of D[X], if and only if Kr(D, v) is a flat D[X]-module. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free