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Let $K$ be a field and $S = K[x_1,dots,x_n]$ be a polynomial ring over $K$. We discuss the behaviour of the extremal Betti numbers of the class of squarefree strongly stable ideals. More precisely, we give a numerical characterization of the possible extremal Betti numbers (values as well as positions) of such a class of squarefree monomial ideals.
Let $R = mathbb{K}[x_1, ldots, x_n]$ and $I subset R$ be a homogeneous ideal. In this article, we first obtain certain sufficient conditions for the subadditivity of $R/I$. As a consequence, we prove that if $I$ is generated by homogeneous complete i
Let $S=K[x_1,ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and $Isubset S$ a squarefree monomial ideal. In the present paper we are interested in the monomials $u in S$ belonging to the socle $Soc(S/I^{k})$ of $S/I^{k}$, i.e.,
We compute the minimal primary decomposition for completely squarefree lexsegment ideals. We show that critical squarefree monomial ideals are sequentially Cohen-Macaulay. As an application, we give a complete characterization of the completely squar
We study the extremal Betti numbers of the class of $t$--spread strongly stable ideals. More precisely, we determine the maximal number of admissible extremal Betti numbers for such ideals, and thereby we generalize the known results for $tin {1,2}$.
Let $K$ be a field and let $S=K[x_1,dots,x_n]$ be a standard polynomial ring over a field $K$. We characterize the extremal Betti numbers, values as well positions, of a $t$-spread strongly stable ideal of $S$. Our approach is constructive. Indeed, g