强 Gorenstein 平坦维数

Strongly Gorenstein Flat Dimensions

中文关键词:  强Gorenstein平坦模  强Gorenstein平坦维数  凝聚环  直积  (几乎)优越扩张.

英文关键词:strongly Gorenstein flat module  strongly Gorenstein flat dimension  coherent ring  direct product  (almost) excellent extension.

中文摘要:

      文章讨论了环和模的强 Gorenstein平坦维数.证明了凝聚环上强Gorenstein平坦维数的良好性质.将著名的Hilbert基定理推广到环的强Gorenstein平坦维数上并讨论了环的直积和(几乎)优越扩张的强Gorenstein平坦维数.

英文摘要:

      This article is concerned with the strongly Gorenstein flat dimensions of modules and rings. We show this dimension has nice properties when the ring is coherent, and extend the well-known Hilbert's syzygy theorem to the strongly Gorenstein flat dimensions of rings. Also, we investigate the strongly Gorenstein flat dimensions of direct products of rings and (almost) excellent extensions of rings.