共查询到20条相似文献,搜索用时 15 毫秒
1.
Kazufumi Eto 《manuscripta mathematica》2002,109(4):455-463
In this paper, we will show that a lattice ideal is a complete intersection if and only if its binomial arithmetical rank
equals its height, if the characteristic of the base field k is zero. And we will give the condition that a binomial ideal equals a lattice ideal up to radical in the case of char k=0. Further, we will study the upper bound of the binomial arithmetical rank of lattice ideals and give a sharp bound for the
lattice ideals of codimension two.
Received: 12 June 2001 / Revised version: 22 July 2002 相似文献
2.
3.
Using a generalized notion of matching in a simplicial complex and circuits of vector configurations, we compute lower bounds for the minimum number of generators, the binomial arithmetical rank and the A-homogeneous arithmetical rank of a lattice ideal. Prime lattice ideals are toric ideals, i.e. the defining ideals of toric varieties. 相似文献
4.
The Riemann–Roch theorem on a graph G is related to Alexander duality in combinatorial commutative algebra. We study the lattice ideal given by chip firing on G and the initial ideal whose standard monomials are the G-parking functions. When G is a saturated graph, these ideals are generic and the Scarf complex is a minimal free resolution. Otherwise, syzygies are obtained by degeneration. We also develop a self-contained Riemann–Roch theory for Artinian monomial ideals. 相似文献
5.
We study the concept of intuitionistic fuzzy sublattices and intuitionistic fuzzy ideals of a lattice. Some characterization
and properties of these intuitionistic fuzzy sublattices and ideals are established. Also we introduce the sum and product
of two intuitionistic fuzzy ideals and prove that the sum and product of two Intuitionistic fuzzy ideals of a distributive
lattice is again an intuitionistic fuzzy ideal. Moreover, we study the properties of intuitionistic fuzzy ideals under lattice
homomorphism. 相似文献
6.
Summary In a recent survey article, G. Grätzer and E. T. Schmidt raise the problem when is the ideal lattice of a sectionally complemented chopped lattice sectionally complemented. The only general result is a 1999 lemma of theirs, stating that if the finite chopped lattice is the union of two ideals that intersect in a two-element ideal U, then the ideal lattice of M is sectionally complemented. In this paper, we present examples showing that in many ways their result is optimal. A typical result is the following: For any finite sectionally complemented lattice U with more than two elements, there exists a finite sectionally complemented chopped lattice M that is (i) the union of two ideals intersecting in the ideal U; (ii) the ideal lattice of M is not sectionally complemented. 相似文献
7.
We give a Gröbner basis for the ideal of 2-minors of a 2 × n utiatrix of linear forms. The minimal free resolution of such an ideal is obtained in [4] when the corresponding Kronecker-Weierstrass normal form has no iiilpotent blocks. For the general case, using this result, the Grobner basis and the Eliahou-Kervaire resolution for stable monomial ideals, we obtain a free resolution with the expected regularity. For a specialization of the defining ideal of ordinary pinch points, as a special case of these ideals, we provide a minimal free resolution explicitly in terms of certain Koszul complex. 相似文献
8.
In this paper,we initiate a study of S-fuzzy ideal(filter) of a lattice where S stands for a meet semilattice.A S-fuzzy prime ideal(filter) of a lattice is defined and it is proved that a S-fuzzy ideal(filter) of a lattice is S-fuzzy prime ideal(filter) if and only if any non-empty α-cut of it is a prime ideal(filter).Stone's theorem for a distributive lattice is extended by considering S-fuzzy ideals(filters). 相似文献
9.
10.
In the present paper, we deal with a class of R
1-ideals of cancellative positive partial abelian monoids (CPAMs). We prove that, for I being an R
1-ideal of a CPAM P, P/I is a CPAM. The lattice of congruence relations associated with R
1-ideals is a sublattice of the lattice of all equivalence relations. Finally, we prove that an intersection of two Riesz ideals
is a Riesz ideal and that the lattice of Riesz ideals is a sublattice of the lattice of all ideals.
Received March 19, 1999; accepted in final form December 16, 1999. 相似文献
11.
Our main objective is to study properties of a fuzzy ideals(fuzzy dual ideals).A study of special types of fuzzy ideals(fuzzy dual ideals) is also furnished.Some properties of a fuzzy ideals(fuzzy dual ideals) are furnished.Properties of a fuzzy lattice homomorphism are discussed.Fuzzy ideal lattice of a fuzzy lattice is defined and discussed.Some results in fuzzy distributive lattice are proved. 相似文献
12.
13.
《Quaestiones Mathematicae》2013,36(7):919-937
AbstractPre-Riesz spaces are ordered vector spaces which can be order densely embedded into vector lattices, their so-called vector lattice covers. Given a vector lattice cover Y for a pre-Riesz space X, we address the question how to find vector lattice covers for subspaces of X, such as ideals and bands. We provide conditions such that for a directed ideal I in X its smallest extension ideal in Y is a vector lattice cover. We show a criterion for bands in X and their extension bands in Y as well. Moreover, we state properties of ideals and bands in X which are generated by sets, and of their extensions in Y. 相似文献
14.
The index of a graded ideal measures the number of linear steps in the graded minimal free resolution of the ideal. In this paper, we study the index of powers and squarefree powers of edge ideals. Our results indicate that the index as a function of the power of an edge ideal I is strictly increasing if I is linearly presented. Examples show that this needs not to be the case for monomial ideals generated in degree greater than two. 相似文献
15.
Thérèse Merlier 《Semigroup Forum》1972,5(1):236-242
In this paper, we establish several properties of the lattice of ideals of a nilpotent semigroup. In particular, we characterize
the finite nilpotent semigroups by the length of this lattice, and we generalize a theorem of T. Tamura and M. Yamada [5],
concerning the ideal extension of a nilpotent semigroup by a null semigroup.
相似文献
16.
As a sequel to [2] and [15] we investigate ideal properties focusing on subtractive varieties. Here we probe the relations
between congruences and ideals in subtractive varieties, in order to give some means to recover the congruence structure from
the ideal structure. To do so we consider mainly two operators from the ideal lattice to the congruence lattice of a given
algebra and we classify subtractive varieties according to various properties of these operators. In the last section several
examples are discussed in details.
Received May 23, 1996; accepted in final form November 25, 1996. 相似文献
17.
SEMIGROUPS CHARACTERIZED BY THEIR FUZZY IDEALS 总被引:5,自引:2,他引:3
SEMIGROUPSCHARACTERIZEDBYTHEIRFUZZYIDEALSJ.AhsanandK.Saifullah(DepartmentofMathematicalSciencesKingFahdUniversityofPetroleuma... 相似文献
18.
We introduce a monomial ideal whose standard monomials encode the vertices of all fibers of a lattice. We study the minimal generators, the radical, the associated primes and the primary decomposition of this ideal, as well as its relation to initial ideals of lattice ideals. 相似文献
19.
HE Peng-fei YANG Yong-wei XIN Xiao-long 《数学季刊》2014,(3):381-391
In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal(filter) which is a generalized intuitionistic fuzzy ideal(filter) of a lattice and study some related properties of such ideals(filters). 相似文献
20.
In this paper we consider monomial localizations of monomial ideals and conjecture that a monomial ideal is polymatroidal if and only if all its monomial localizations have a linear resolution. The conjecture is proved for squarefree monomial ideals where it is equivalent to a well-known characterization of matroids. We prove our conjecture in many other special cases. We also introduce the concept of componentwise polymatroidal ideals and extend several of the results known for polymatroidal ideals to this new class of ideals. 相似文献