Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE w-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS

  • WANG, FANGGUI (COLLEGE OF MATHEMATICS AND SOFTWARE SCIENCE SICHUAN NORMAL UNIVERSITY) ;
  • QIAO, LEI (COLLEGE OF MATHEMATICS AND SOFTWARE SCIENCE SICHUAN NORMAL UNIVERSITY)
  • Received : 2014.09.08
  • Published : 2015.07.31
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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 $Pr\ddot{u}fer$ v-multiplication domain if and only if w-w.gl.dim(R) ${\leq}1$. 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]) = w-w.gl.dim(R).

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