A remark on sequentially Cohen-Macaulay monomial ideals

Let R=K[x_۱,\ldots,x_n] be the polynomial ring in n variables over a field K. We show that if G is a connected graph with a basic ۵-cycle C, then G is a sequentially Cohen-Macaulay graph if and only if there exists a shedding vertex x of C such that G\setminus x and G\setminus N[x] are sequentially Cohen-Macaulay graphs. Furthermore, we study the sequentially Cohen-Macaulay and Castelnuovo-Mumford regularity of square-free monomial ideals in some special cases.

کلیدواژه ها:

Sequentially Cohen-Macaulay ، Monomial ideals ، Shedding vertex