Depth in a pathological case

Publication date: 15 December 2016

Abstract: Let

I

be a squarefree monomial ideal of a polynomial algebra over a field minimally generated by

f_{1}, . . ., f_{r}

of degree

d g e q 1

, and a set

E

of monomials of degree

g e q d + 1

. Let

J s u b s e t n e q I

be a squarefree monomial ideal generated in degree

g e q d + 1

. Suppose that all squarefree monomials of

I s e t m i n u s (J c u p E)

of degree

d + 1

are some least common multiples of

f_{i}

. If

J

contains all least common multiples of two of

(f_{i})

of degree

d + 2

then

d e p t h_{S} I / J l e q d + 1

and Stanley's Conjecture holds for

I / J

.