Let $ G $ be a graph with $ n $ vertices and $ S=\mathbb {K}[x_1,\dots, x_n] $ be the
polynomial ring in $ n $ variables over a field $\mathbb {K} $. Assume that $ J (G) $ is the …

This paper addresses the problem of comparing minimal free resolutions of symbolic powers
of an ideal. Our investigation is focused on the behavior of the function\, depth\, R/I^(t)=\dim …

We prove that for m⩾ 3, the symbolic power IΔ (m) of a Stanley–Reisner ideal is Cohen–
Macaulay if and only if the simplicial complex Δ is a matroid. Similarly, the ordinary power …

In this paper, we use polarization to study the behavior of the depth and regularity of a
monomial ideal I, locally at a variable xi, when we lower the degree of all the highest powers …

The behavior of depth functions of cover ideals of unimodular hypergraphs Page 1 DOI:
10.4310/ARKIV.2017.v55.n1.a4 c 2017 by Institut Mittag-Leffler. All rights reserved Ark. Mat., 55 …

Let KK be a field and S= K x_1,\dots, x_n S= K x 1,⋯, xn be the polynomial ring in n variables
over K K. Let G be a graph with n vertices. Assume that I= I (G) I= I (G) is the edge ideal of G …

Over the last 25 years the study of algebraic, homological and combinatorial properties of
powers of ideals has been one of the major topics in Commutative Algebra. In this article, we …

We show that the second power of the cover ideal of a path graph has linear quotients. To
prove our result we construct a recursively defined order on the generators of the ideal …

In 1982, Stanley predicted a combinatorial upper bound for the depth of any finitely
generated multigraded module over a polynomial ring. The predicted invariant is now called …

Stability of depth functions of cover ideals of balanced hypergraphs Page 1 Journal of Algebra
and Its Applications Vol. 19, No. 3 (2020) 2050055 (13 pages) c© World Scientific Publishing …