Finiteness of Gorenstein injective dimension of modules
Finiteness of Gorenstein injective dimension of modules
复制标题
DOI：
10.1090/s0002-9939-09-09784-6
复制
发表时间：
2009-01
期刊：
影响因子：
--
通讯作者：
Leila Khatami;M. Tousi;S. Yassemi
中科院分区：
文献类型：
--
作者：
Leila Khatami;M. Tousi;S. Yassemi
诺特环上模的单射维数的乔伊纳德公式被扩展到 Gorenstein 单射维数。具体来说，如果 M 是交换诺特环 R 上的有限正 Gorenstein 内射维数的模，则其 Gorenstein 内射维数为深度 Rp ― 宽度 R p M p 的上界，其中 p 贯穿 R 的所有素理想。还证明，如果 M 是有限生成且非零，则其 Gorenstein 内射维数等于基环的深度。这概括了单射维数的经典巴斯公式。
The Chouinard formula for the injective dimension of a module over a noetherian ring is extended to Gorenstein injective dimension. Specifically, if M is a module of finite positive Gorenstein injective dimension over a commutative noetherian ring R, then its Gorenstein injective dimension is the supremum of depth Rp ― width R p M p , where p runs through all prime ideals of R. It is also proved that if M is finitely generated and non-zero, then its Gorenstein injective dimension is equal to the depth of the base ring. This generalizes the classical Bass formula for injective dimension.