BCK-代数的Ω-模糊正定关联理想

给定一个集合Ω,引入了BCK-代数的Ω-模糊正定关联理想的概念,给出了一些恰当的例子,讨论了BCK-代数的Ω-模糊理想与Ω-模糊正定关联理想的关系.利用模糊正定关联理想,刻画了Ω-模糊正定关联理想.反之,模糊正定关联理想通过Ω-模糊正定关联理想来构造.证明了Ω-模糊正定关联理想(Ω-模糊理想)的同态原象仍是Ω-模糊理想(Ω-模糊理想).     

半群的(∈,∈∨q(λ,μ))-模糊n伪理想与Drazin半群的刻画

给出半群的模糊n伪理想,广义模糊n伪理想,(∈,∈∨q(λ,μ))-模糊n伪理想的定义,同时讨论了(∈,∈∨q(λ,μ))-模糊n伪左理想(右理想,理想)和广义模糊n伪左理想(右理想,理想)的等价刻画.还利用半群的广义模糊子系统来刻画Drazin半群的结构.     

The stable set of associated prime ideals of a polymatroidal ideal

The associated prime ideals of powers of polymatroidal ideals are studied, including the stable set of associated prime ideals of this class of ideals. It is shown that polymatroidal ideals have the persistence property and for transversal polymatroids and polymatroidal ideals of Veronese type the index of stability and the stable set of associated ideals is determined explicitly.     

BCI代数的软关联理想和软正定关联理想

给出BCI代数的软关联理想和软正定关联理想的概念,讨论软理想、软关联理想和软正定关联理想三者之间的关系,研究了两个软关联理想(软正定关联理想)的扩展交、限制交、限制并和限制差分的性质。     

UNIQUE FACTORIZATION AND BIRTH OF ALMOST PRIMES

ABSTRACT

In studying unique factorization of domains we encountered a property of ideals. Using that we define the notion of almost prime ideals and prove that in Noetherian domains almost prime ideals are primary. We also prove that in a regular domain almost primes are precisely primes. Further, we define strictly nonprime ideals and study some inter relations between almost prime ideals, strictly nonprime ideals and factorization of ideals.     

BCK/BCI-代数的Ω-模糊点理想

给定Ω-集合，引入BCK／BCI-代数的Ω-模糊点理想的概念，给出合适的例子。同时，将Ω-模糊点理想与模糊点理想进行相互刻画。     

Criteria for Componentwise Linearity

We establish characteristic-free criteria for the componentwise linearity of graded ideals. As applications, we classify the componentwise linear ideals among the Gorenstein ideals, the standard determinantal ideals, and the ideals generated by the submaximal minors of a symmetric matrix.     

BCI-代数的Fuzzy广义结合理想

引入了BCI-代数的fuzzy广义结合理想的概念，给出了它的一种刻画，讨论了fuzzy广义结合理想与其它fuzzy理想的关系，并利用fuzzy广义结合理想得到了拟结合BCI-代数成为结合BCI-代数的几个特征。     

Fuzzy Ideals and Fuzzy Distributive Lattices

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.     

半群的完全素和素模糊理想

通过由模糊点生成的模糊理想给出了半单半群的刻画。同时也刻画了两类半群：一类是所有模糊理想是素理想。另一类是所有模糊理想为安全素理想。     

Reverse lex ideals

We study reverse lex ideals in a polynomial ring, and compare their properties to those of lex ideals. In particular we provide an analogue of Green's Theorem for reverse lex ideals. We also compare the Betti numbers of strongly stable and square-free strongly stable monomial ideals to those of reverse lex ideals.     

Ideals that are an irredundant union of principal ideals

We investigate ideals of a commutative ring that are an irredundant union of principal ideals. Special attention is paid to prime ideals that are a finite union of principal ideals.     

Fuzzy半群中的Fuzzy理想

本文先引入Ｆｕｚｚｙ半群中Ｆｕｚｚｙ理想的概念，进而讨论它们的一些代数性质，推广了前人的一些结果。     

Certain variants of multipermutohedron ideals

Multipermutohedron ideals have rich combinatorial properties. An explicit combinatorial formula for the multigraded Betti numbers of a multipermutohedron ideal and their Alexander duals are known. Also, the dimension of the Artinian quotient of an Alexander dual of a multipermutohedron ideal is the number of generalized parking functions. In this paper, monomial ideals which are certain variants of multipermutohedron ideals are studied. Multigraded Betti numbers of these variant monomial ideals and their Alexander duals are obtained. Further, many interesting combinatorial properties of multipermutohedron ideals are extended to these variant monomial ideals.     

Freiman ideals

In this paper we study the Freiman inequality for the least number of generators of the square of an equigenerated monomial ideal. Such an ideal is called a Freiman ideal if equality holds in the Freiman inequality. We classify all Freiman ideals of maximal height, the Freiman ideals of certain classes of principal Borel ideals, the Hibi ideals which are Freiman, and classes of Veronese type ideals which are Freiman.     

Ideals in Algebras of Unbounded Operators

A general procedure is given to get ideals in algebras of unbounded operators starting with ideals in ??(??). Algebraical and topological properties of ideals obtained in this manner from the well-known symmetrically-normed ideals S_?(??) are described.     

Intuitionistic fuzzy sublattices and ideals

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.     

Semiprime Ideals and Separation Theorems for Posets

The concept of a semiprime ideal in a poset is introduced. The relations between the semiprime (prime) ideals of a poset and the ideals of the set of all ideals of the poset are established. A result analogous to Separation Theorem is obtained in respect of semiprime ideals. Further, a generalization of Stone’s Separation Theorem for posets is obtained in respect of prime ideals. Some counterexamples are also given.      

Constructible Ideals

Based on the study of simplicial complexes, one may naturally define the constructible monomial ideals. We connect the square-free constructible ideal with the Stanley–Reisner ideal of the Alexander dual associated to a constructible simplicial complex. We give some properties of constructible ideals, and we compute the Betti numbers. We prove that all monomial ideals with linear quotients are constructible ideals. We also show that all constructible ideals have a linear resolution.