相对于半对偶化模的环的Gorenstein整体维数

GORENSTEIN GLOBAL DIMENSIONS OF RINGS WITH RESPECT TO A SEMIDUALIZING MODULE

设R是交换环且C是一个半对偶化模.我们证明了R的整体G_(C)-投射维数和整体G_(C)-内射维数是相等的.我们还研究了R的整体G_(C)-平坦维数的性质.

Let R be a commutative ring and C a semidualizing module.We prove that the global G_(C)-projective dimension and the global G_(C)-injective dimension of R are identical.We also investigate the properties of the global G_(C)-flat dimension of R.