2021/06/22 by Zhang, Xiaolei, Qi, Wei
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2106.11474
Let R be a commutative ring with identity and S a multiplicative subset of R. First, we introduce and study the S-projective dimensions and S-injective dimensions of R-modules, and then explore the S-global dimension S-gl.dim(R) of a commutative ring R which is defined to be the supremum of S-projective dimensions of all R-modules. Finally, we investigated the S-global dimension of factor rings and polynomial rings.