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k-Decomposable Monomial Ideals

In this paper we introduce a class of monomial ideals, called k-decomposable ideals. It is shown that the class of k-decomposable ideals is contained in the class of monomial ideals with linear quotients, and when k is large enough, the class of k-decomposable ideals is equal to the class of ideals with linear quotients. In addition, it is shown that a d-dimensional simplicial complex is k-decomposable if and only if the Stanley-Reisner ideal of its Alexander dual is a k-decomposable ideal, where k ≤ d. Moreover, it is shown that every k-decomposable ideal is componentwise k-decomposable.

World Scientific Pub Co Pte Lt

Rahim Rahmati-Asghar Siamak Yassemi

Algebra Colloquium

2015

Title: k-Decomposable Monomial Ideals

Description:

In this paper we introduce a class of monomial ideals, called k-decomposable ideals.

It is shown that the class of k-decomposable ideals is contained in the class of monomial ideals with linear quotients, and when k is large enough, the class of k-decomposable ideals is equal to the class of ideals with linear quotients.

In addition, it is shown that a d-dimensional simplicial complex is k-decomposable if and only if the Stanley-Reisner ideal of its Alexander dual is a k-decomposable ideal, where k ≤ d.

Moreover, it is shown that every k-decomposable ideal is componentwise k-decomposable.

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