Rings with monomial relations having linear resolutions
Rings with monomial relations having linear resolutions
复制标题
具有线性分辨率的单项关系环
DOI：
10.1016/0022-4049(85)90011-8
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发表时间：
1985
影响因子：
0.8
通讯作者：
R. Fröberg
中科院分区：
文献类型：
--
作者：
R. Fröberg
在本注释中，具有单项式关系的环意味着具有表示形式 k [X,,..., X,]/(M,,..., Al,) 的代数，其中 k 是一个域，Mi'S 是 Xj 中的单项式。本文的目的是给出单项式关系环具有线性分辨率的充要条件。关键点是将问题简化为具有无平方单项关系的环的情况，然后将这种环的 Koszul 复形的同源性与某些相关单纯复形的单纯同源性之间的联系。这种联系还给出了单纯复形的组合性质的一些结果。它还给出了该环成为科恩-麦考利环的精确条件。
A ring with monomial relations will in this note mean an algebra with a presentation k [X,,..., X,]/(M,,..., Al,), where k is a field and the Mi’S are monominals in the Xj’s. The aim of this note is to give a necessary and sufficient condition for a ring with monomial relations to have a linear resolution. The crucial points will be a reduction of the problem to the case of rings with squarefree monomial relations, and then a connection between the homology of the Koszul complex for such a ring and the simplicial homology for some associated simplicial complexes. This connection also gives some results of combinatorial nature for simplicial complexes. It also yields a precise condition for the ring to be Cohen-Macaulay.