Kronecker函数环对PvMD的一个新刻画

A New Characterization of PvMDS by Kronecker Function Rings

设R是整环,若R是整闭的,则R是Prüfer整环当且仅当Kr(R,b)是平坦R[X]-模;当且仅当Kr(R,b)是平坦R-模(Aaderson D F,Bobbs D E.J Pure Appl Algebra,1989,61:107-122.).给出这一定理在w-版本下的陈述形式,即若R是整闭整环,则R是P v MD当且仅当Kr(R,v c)是w(R[X])-平坦R[X]-模;当且仅当Kr(R,v c)是w-平坦R-模.

In this paper,we show that if R is integrally closed,then R is a P v MD if and only if Kr(R,v c)is a w(R[X])-flat R[X]-module;if and only if Kr(R,v c)is a w-flat R-module.This is a generalization of(Aaderson D F,Bobbs D E.J Pure Appl Algebra,1989,61:107-122.)that if R is integrally closed,then R is a Prüfer domain if and only if Kr(R,b)is a flat R[X]-module;if and only if Kr(R,b)is a flat R-module.