Syzygy Modules for Noetherian Rings
Syzygy Modules for Noetherian Rings
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DOI：
10.1006/jabr.1996.0212
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发表时间：
1996-07
影响因子：
0.9
通讯作者：
M. Auslander;I. Reiten
中科院分区：
文献类型：
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作者：
M. Auslander;I. Reiten
全文是一个双面诺瑟环，并对有限生成模的范畴进行建模。对于每一个整数k) 0我们k Ž。用模表示模的完整子范畴，其对象是模中的C，是模中的模的第k次合，即在ky10模中存在一个精确序列0ªCªPªPªBª0与P个射影模。虽然i模块的投影分辨率已被广泛研究，但对k Ž似乎知之甚少。子范畴的模。关于这些范畴的一个已知的一般性质是它们对w x k的模是协变有限的
Throughout this paper is a twosided noetherian ring and mod the category of finitely generated-modules. For each integer k) 0 we k Ž. denote by mod the full subcategory of mod whose objects are the C in mod which are the kth syzygies of modules in mod, that is, for which there is an exact sequence 0 ª C ª P ª ª P ª B ª 0 in ky1 0 mod with the P projective modules. While projective resolutions of i modules have been studied extensively, little seems to be known about the k Ž. subcategories mod of mod. One of the few general properties known about these categories is that they are covariantly finite in mod w x k