Torsionfree dimension of modules and self-injective dimension of rings
Torsionfree dimension of modules and self-injective dimension of rings
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DOI：
10.18910/4508
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发表时间：
2009-06
影响因子：
0.4
通讯作者：
Chonghui Huang;Zhaoyong Huang
中科院分区：
文献类型：
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作者：
Chonghui Huang;Zhaoyong Huang
设R是左、右Noether环。我们引入了非线性生成R-模的无挠维数的概念。对任意n 0，证明了R是自内射维数至多为n的Gorenstein环当且仅当每个R-R生成左R-模和R-R生成右R-模的torsionfree维数至多为n，当且仅当每个R-R生成左（或右）R-模的Gorenstein维数至多为n.对任意n 1，研究了具有Ext i R（M，R）0的n-生成R-模M对任意1 i n的性质.然后研究了这些性质与R的自内射维数之间的关系。
Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated R-modules. For any n 0, we prove that R is a Gorenstein ring with self-injective dimension at most n if and only if every finitely generated left R-module and every finitely generated right R-module have torsionfree dimension at most n, if and only if every finitely generated left (or right) R-module has Gorenstein dimension at most n. For any n 1, we study the properties of the finitely generated R-modules M with Ext i R (M, R) 0 for any 1 i n. Then we investigate the relation between these properties and the s elf-injective dimension of R.