Initially regular sequences and depths of ideals

JOURNAL OF ALGEBRA

卷:559

Article

Fouli, Louiza¹  Huy Tai Ha²  Morey, Susan³ 

[1] New Mexico State Univ, Dept Math Sci, POB 30001,Dept 3MB, Las Cruces, NM 88003 USA

[2] Tulane Univ, Dept Math, 6823 St Charles Ave, New Orleans, LA 70118 USA

[3] Texas State Univ, Dept Math, 601 Univ Dr, San Marcos, TX 78666 USA

关键词: Regular sequence;    Depth;    Projective dimension;    Monomial ideal;    Edge ideal;    Grobner basis;    Initial ideal;   

DOI  :  10.1016/j.jalgebra.2020.03.027

来源: Elsevier

【 摘 要 】

For an arbitrary ideal I in a polynomial ring R we define the notion of initially regular sequences on R/I. These sequences share properties with regular sequences. In particular, the length of an initially regular sequence provides a lower bound for the depth of R/I when I is homogeneous. Using combinatorial information from the initial ideal of I we construct sequences of linear polynomials that form initially regular sequences on R/I. We identify situations where initially regular sequences are also regular sequences, and we show that our results can be combined with polarization to improve known depth bounds for general monomial ideals. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free