Lexsegment ideals are sequentially Cohen-Macaulay

Abstract

The associated primes of an arbitrary lexsegment ideal $I\subset S=K[x_1,...,x_n]$ are determined. As application it is shown that $S/I$ is a pretty clean module, therefore, $S/I$ is sequentially Cohen-Macaulay and satisfies Stanley's conjecture.

to appear in Algebra Colloquium

Cited by in corpus (4)

• Lexsegment ideals of Hilbert depth 1
• On the minimal graded free resolution of powers of lexsegment ideals
• Monomial ideals of minimal depth and trivial modifications
• Invariants of some classes of monomial ideals