THE w-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS

Title & Authors
THE w-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS
WANG, FANGGUI; QIAO, LEI;

Abstract
In this paper, we introduce and study the w-weak global dimension w-w.gl.dim(R) of a commutative ring R. As an application, it is shown that an integral domain R is a $\small{Pr\ddot{u}fer}$ v-multiplication domain if and only if w-w.gl.dim(R) $\small{{\leq}1}$. We also show that there is a large class of domains in which Hilbert`s syzygy Theorem for the w-weak global dimension does not hold. Namely, we prove that if R is an integral domain (but not a field) for which the polynomial ring R[x] is w-coherent, then w-w.gl.dim(R[x])
Keywords
GV-torsionfree module;w-module;w-flat module;w-flat dimension;w-weak global dimension;
Language
English
Cited by
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3.
A new application of boundary integral behaviors of harmonic functions to the least harmonic majorant, Boundary Value Problems, 2017, 2017, 1
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