We extend the definition of chordal from graphs to clutters. The resulting family generalizes both chordal graphs and matroids, and obeys many of the same algebraic and geometric properties. Specifically, the independence complex of a chordal clutter is shellable, hence sequentially Cohen-Macaulay; and the circuit ideal of a certain complement to such a clutter has a linear resolution. Minimal ...

In this survey paper we first present the main properties of sequentially Cohen-Macaulay modules. Some basic examples are provided to help reader with quickly getting acquainted topic. We then discuss two generalizations notion sequential Cohen-Macaulayness which inspired by a theorem J\"urgen Herzog and third author.

This paper shows that if [Formula: see text] is a homomorphic image of Cohen–Macaulay local ring, then text]-module sequentially generalized and only the difference between Hilbert coefficients arithmetic degrees for all distinguished parameter ideals are bounded.