Homological invariants of unbounded complexes under Frobenius extensions

被引：0
|
作者：
Wu, Dejun [1 ]
Wang, Yongduo [1 ]
机构：
[1] Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Peoples R China
来源：
COMMUNICATIONS IN ALGEBRA | 2023年 / 51卷 / 03期
关键词：
Frobenius extension; Gorenstein flat-cotorsion module; Gorenstein projective dimension; GORENSTEIN FLAT DIMENSION; COVERS;
D O I：
10.1080/00927872.2022.2134407
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let R subset of S be a Frobenius extension of rings and M an S-complex. It is proven that if the Gorenstein projective (injective) dimension of M as an S-complex is finite, then the Gorenstein projective (injective) dimension of M as an S-complex equals the Gorenstein projective (injective) dimension of M as an R-complex. As a corollary one has that if the projective (injective) dimension of M as an S-complex is finite, then the projective (injective) dimension of M as an S-complex equals the projective (injective) dimension of M as an R-complex. This statement extends a known result of Nakayama and Tsuzuku.
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页码：1298 / 1307
页数：10
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