In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I is equal to the projective dimension of R/I in the following cases: (a) I is an almost complete intersection; (b) arithdeg I = reg I ; (c) arithdeg I = indeg I + 1. We also classify all almost complete intersection squarefree monomial ideals in terms of hypergraphs, and use this classification in the proof in ca...

Let A be a finite set of closed rational points in projective space, let I be the vanishing ideal of A , and let D(A ) be the set of exponents of those monomials which do not occur as leading monomials of elements of I . We show that the size of A equals the number of axes contained in D(A ). Furthermore, we present an algorithm for the construction of the Gröbner basis of I (A ), hence also of...

A module is called uniseriat if it has a unique composition series of finite length. A ring (always with 1) is called serial if its right and left free modules are direct sums of uniserial modules. Nakayama, who called these rings generalized uniserial rings, proved [21, Theorem 171 that every finitely generated module over a serial ring is a direct sum of uniserial modules. In section one we g...

When a cone is added to a simplicial complex ∆ over one of its faces, we investigate the relation between the arithmetical ranks of the StanleyReisner ideals of the original simplicial complex and the new simplicial complex ∆′. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of ∆′ equals the projective dimension of the Stanley-Reisner ring of ∆′ if the correspondi...

This paper is concerned with a relationship between the existence of subvarieties of principally polarized abelian varieties (ppav’s) having minimal cohomology class and the (generic) vanishing of certain sheaf cohomology, based on the Generic Vanishing criterion studied in [PP3]. This is in analogy with the well-known equivalence between a subvariety in projective space being of minimal degree...

Let A be a finite set of closed rational points in projective space, let I be the vanishing ideal of A , and let D(A ) be the set of exponents of those monomials which do not occur as leading monomials of elements of I . We show that the size of A equals the number of axes contained in D(A ). Furthermore, we present an algorithm for the construction of the Gröbner basis of I (A ), hence also of...

Abstract. We show that the Hilbert-Kunz multiplicity is a rational number for an R+−primary homogeneous ideal I = (f1, . . . , fn) in a twodimensional graded domain R of finite type over an algebraically closed field of positive characteristic. Moreover we give a formula for the HilbertKunz multiplicity in terms of certain rational numbers coming from the strong Harder-Narasimhan filtration of ...

Let R be a commutative ring with the unit element. It is shown that an ideal I in pure if and only Ann(f) + = for all f ∈ I. If J trace of projective R-module M, we prove generated by “coordinates” M JM M. These lead to few new results alternative proofs some known results.

We study ideal cotorsion pairs associated to almost exact structures in extension closed subcategories of triangulated categories. This approach allows us extend the recent approximation theory developed by Fu, Herzog et al. for categories above mentioned context. In last part paper we apply order projective classes (in particular localization or smashing subcategories) compactly generated

We prove that the diametral diameter two properties are inherited by F-ideals (e.g., M-ideals). On other hand, these lifted from an M-ideal to superspace under strong geometric assumptions. also show all of stable formation corresponding Köthe–Bochner spaces $$L_p$$ -Bochner spaces). Finally, we investigate when projective tensor product Banach has some property.