Some algebraic invariants related to mixed product ideals

We compute some algebraic invariants (e.g. depth, Castelnuovo-Mumford regularity) for a special class of monomial ideals, namely the ideals of mixed products. As a consequence, we characterize the Cohen-Macaulay ideals of mixed products. Received: 25 October 2007     

Generalized mixed product ideals

We consider classes of ideals which generalize the mixed product ideals introduced by Restuccia and Villarreal (see [5]), and also generalize the expansion construction by Bayati and Herzog [1]. We compute the minimal graded free resolution of generalized mixed product ideals and show that the regularity of a generalized mixed product ideal coincides with the regularity of the monomial ideal by which it is induced.     

Cardinal invariants associated with Fubini product of ideals

We prove some results displaying the relationship between Fubini product of ideals and its factor ideals, and study a partial order using the cardinal invariant of the continuum. The relationships among transitive cardinal invariants of abelian group are also investigated.     

Betti numbers of mixed product ideals

We compute the Betti numbers of the resolution of a special class of square-free monomial ideals, the ideals of mixed products. Moreover when these ideals are Cohen-Macaulay we calculate their type. Received: 9 March 2008     

On alternating invariants and Hilbert ideals

In a paper on F-rationality [J. Algebra 176 (1995) 824–860] Donna Glassbrenner showed that over a field of odd characteristic p the Hilbert ideals of the tautological representations of the symmetric group Σ_n and alternating group A_n coincide if . She asked if this was always the situation in the modular case. We answer this in the affirmative using Macaulay's theory of irreducible ideals in polynomial algebras: a somewhat forgotten bywater of commutative algebra. As a bonus, the method yields applications back to the original question of F-rationality studied in [J. Algebra 176 (1995) 824–860].     

Algebraic and homological properties of generalized mixed product ideals

Archiv der Mathematik - Algebraic and homological invariants of generalized mixed product ideals induced by a monomial ideal are studied. We characterize the Cohen–Macaulay generalized mixed...     

BCI-代数中的几种理想

BCI－代数中的理想是一个极其重要的概念，本文引入两类不同的理想，即广义结合理想与拟右交错理想，研究了他们与思想，结合理想，P－理想的关系，并用广义结合理想子代数，刻画了广义结合BCI－代数，指明了拟右交错理想与结合理想的不同之处，用拟右交错理想刻画了拟右交错BCI－代数。     

On some coarse shape invariants

The author and N. Ugleši? have recently introduced a new classification of topological spaces, strictly coarser than the shape type classification. The corresponding coarse shape theory is founded on the coarse shape category. In this paper several topological and shape invariants are considered with respect to the coarse shape. It is shown that the coarse shape domination preserves connectedness, shape dimension, movability, n-movability and strong movability. Further, stability is a coarse shape invariant. Moreover, the coarse shape and shape coincide on the class of stable spaces.     

Good invariants for bad ideals

We generalize the notion of the Segre class of ideals defined by Murthy and obtain various analogous results using the theory of the Euler class groups.     

On the grade of some ideals

An additivity formula is obtained for the grade of an ideal in a residue ring R/I, where I is a perfect ideal. This result is then applied to compute the grade of ideals of linear (inhomogeneous) polynomials. Further results on the homological rigidity of the conormal module I/I² are pointed out. Finally, an elementary proof is given of a result of Buchsbaum concerning the grade of ideals of minors of a matrix.Partially supported a CNPq grantPartially supported by NSF and CNPq grants     

On the direct product conjecture for sigma invariants

We show that the direct product conjecture for ⁿ(G; ), whereG is the direct product of two groups of type FP_n, holds forn = 3 and give counterexamples for n 4. Previously, counter-exampleswere known only for a related conjecture involving the homotopical-invariants, where the conjecture already fails for n 3.     

Asymptotic invariants constructed from generic initial ideals

Generic initial ideals (gins for short) were systematically introduced by Galligo in 1974 under the name of Grauert invariants since they appeared apparently first in works of Grauert and Hironaka. Ever since they have been of interest in commutative algebra and indirectly in algebraic geometry. Recently, Mayes in a series of articles associated with gins of graded families of ideals geometric objects called limiting shapes. The construction resembles that of Okunkov bodies but there are some differences as well. This work is motivated by Mayes articles and explores the connections between gins, limiting shapes, and some asymptotic invariants of homogeneous ideals which are associated with the gins, for example, asymptotic regularity, Waldschmidt constant and some new invariants, which seem relevant from geometric point of view.     

Some interpretations for algebraic invariants of edge ideals of hypergraphs via combinatorial invariants

Abstract

The present work is concerned with characterizing some algebraic invariants of edge ideals of hypergraphs. To this aim, first, we introduce some kinds of combinatorial invariants similar to matching numbers for hypergraphs. Then we compare them to each other and to previously existing ones. These invariants are used for characterizing or bounding some algebraic invariants of edge ideals of hypergraphs such as graded Betti numbers, projective dimension and Castelnouvo–Mumford regularity.

Communicated by Jason P. Bell     

On some local cohomology invariants of local rings

Let A be a commutative Noetherian local ring containing a field of characteristic p>0. The integer invariants λ _i,j (A) have been introduced in an old paper of ours. In this paper we completely describe λ _d,d (A) where d=dimA in terms of the topology of SpecA. NSF support through grant DMS-0202176 is gratefully acknowledged     

On some computational algorithms forn-fold ideals in BCK-algebras

This paper is devoted to thefoldness theory of implicative ideals in BCK-algebras. We use the fuzzy point concept to give some characterizations of fuzzyn-fold implicative ideals and establish some relationships with variousn-fold ideals. We also construct some algorithms for studying the foldness of implicative ideals in BCK-algebras.     

On the continuity of scales of some operator ideals

The continuity of p-absolutely summing and p-nuclear norms in the corresponding scales of Banach operator ideals is studied. Bibliography: 17 titles. Translated fromProblemy Matematicheskogo Analiza, No. 19, 1999, pp. 193–214.     

Cones and asymptotic invariants of multigraded systems of ideals

We show that the only regularity property satisfied by asymptotic invariants of abstract multigraded systems of ideals is convexity, which is imposed formally.