Syzygies of Cohen-Macaulay modules and Grothendieck groups
Syzygies of Cohen-Macaulay modules and Grothendieck groups
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Cohen-Macaulay 模和 Grothendieck 群的 Syzygies
DOI：
10.1016/j.jalgebra.2017.06.038
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Toshinori Kobayashi
中科院分区：
文献类型：
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作者：
Toshinori Kobayashi
本文研究了Butler和Auslander-Reiten定理的匡威。证明了当Auslander-Reiten序列生成Cohen-Macaulay生成模的Grothendieck群的关系时，具有孤立奇点的Cohen-Macaulay局部环的Cohen-Macaulay模的合之积的不可分解和的同构类仅为1/2个.这扩展了平松最近的一个结果，它在Gorenstein的情况下给出了肯定的答案，Auslander的猜想。
We study the converse of a theorem of Butler and Auslander–Reiten. We show that a Cohen–Macaulay local ring with an isolated singularity has only finitely many isomorphism classes of indecomposable summands of syzygies of Cohen–Macaulay modules if the Auslander–Reiten sequences generate the relation of the Grothendieck group of finitely generated modules. This extends a recent result of Hiramatsu, which gives an affirmative answer in the Gorenstein case to a conjecture of Auslander.