Structural decomposition of monomial resolutions

JOURNAL OF ALGEBRA

卷:516

Article

Alesandroni, Guillermo¹ 

[1] Wake Forest Univ, Dept Math, 1834 Wake Forest Rd, Winston Salem, NC 27109 USA

关键词: Taylor resolution;    Monomial ideal;    Minimal free resolution;    Projective dimension;    Multigraded Betti number;   

DOI  :  10.1016/j.jalgebra.2018.09.003

来源: Elsevier

【 摘 要 】

We express the multigraded Betti numbers of an arbitrary monomial ideal in terms of the multigraded Betti numbers of two basic classes of ideals. This decomposition has multiple applications. In some concrete cases, we use it to construct minimal resolutions of classes of monomial ideals; in other cases, we use it to compute projective dimensions. To illustrate the effectiveness of the structural decomposition, we give a new proof of a classic theorem by Charalambous that states the following: let k be a field, and M an Artinian monomial ideal in S = k[x(1),...,x(n)]; then, for all i, b(i)(S/M) >= ((n)(i)). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free