Oriented tree diagram Lie algebras and their abelian ideals

We introduce oriented tree diagram Lie algebras which are generalized from Xu＇s both upward and downward tree diagram Lie algebras, and study certain numerical invariants of these algebras related to abelian ideals.     

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。     

BCI-代数的余模糊理想

在BCI-代数中引入了余模糊理想的概念,讨论了它的某些性质,研究了BCI-代数的模糊理想和余模糊理想的关系.特别是,给出了一个如何由一个模糊子集生成一个余模糊理想和闭余模糊理想的过程.     

Universal forcing notions and ideals

Our main result states that a finite iteration of Universal Meager forcing notions adds generic filters for many forcing notions determined by universality parameters. We also give some results concerning cardinal characteristics of the σ-ideals determined by those universality parameters. Both authors acknowledge support from the United States-Israel Binational Science Foundation (Grant no. 2002323). Also, we would like to thank the referee for valuable comments and suggestions concerning the exposition of the paper. This is publication 845 of the second author     

TL-subrings and TL-ideals,Part3:Maximal TL-ideals and ireducible TL-ideals

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MS代数的核理想

本文证明了绝对不可分的MS代数和类布尔代数的每个原理想都是核理想。     

Preserving levels of projective determinacy by tree forcings

We prove that various classical tree forcings—for instance Sacks forcing, Mathias forcing, Laver forcing, Miller forcing and Silver forcing—preserve the statement that every real has a sharp and hence analytic determinacy. We then lift this result via methods of inner model theory to obtain level-by-level preservation of projective determinacy (PD). Assuming PD, we further prove that projective generic absoluteness holds and no new equivalence classes are added to thin projective transitive relations by these forcings.     

Betti numbers of some monomial ideals

In this paper we compute the graded Betti numbers of certain monomial ideals that are not stable. As a consequence we prove a conjecture, stated by G. Fatabbi, on the graded Betti numbers of two general fat points in

     

Decomposition of ideals into pseudo-irreducible ideals

A proper ideal of a commutative ring is called pseudo-irreducible if it cannot be written as a product of two comaximal proper ideals. In this paper, we give a necessary and su?cient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal pseudo-irreducible ideals. Examples of such rings include Laskerian rings, or more generally J-Noetherian rings and ZD-rings. We study when certain classes of rings satisfy this condition.     

Length, multiplicity, and multiplier ideals

Let be an -dimensional regular local ring, essentially of finite type over a field of characteristic zero. Given an -primary ideal of , the relationship between the singularities of the scheme defined by and those defined by the multiplier ideals , with varying in , are quantified in this paper by showing that the Samuel multiplicity of satisfies whenever . This formula generalizes an inequality on log canonical thresholds previously obtained by Ein, Mustata and the author of this paper. A refined inequality is also shown to hold for small dimensions, and similar results valid for a generalization of test ideals in positive characteristics are presented.

     

半环的L-模糊理想的范畴性质

首先给出了半环的L-模糊理想同态的定义,在此基础上较系统地讨论了半环的L-模糊理想范畴的性质,证明了此范畴是半环范畴上的一个拓扑结构,并探讨了其中的等子、拉回和乘积等性质.另一方面,给出了半环的L-模糊理想范畴的逆系统的定义,建立了半环的L-模糊理想范畴中逆系统的逆极限结构.特别是在引入两个逆系统之间映射的基础上,得到了两个逆系统的逆极限之间的极限映射.     

Reduction numbers and initial ideals

The reduction number of a standard graded algebra is the least integer such that there exists a minimal reduction of the homogeneous maximal ideal of such that . Vasconcelos conjectured that where is the initial ideal of an ideal in a polynomial ring with respect to a term order. The goal of this note is to prove the conjecture.

     

Ultrafilters on -their ideals and their cardinal characteristics

For a free ultrafilter on we study several cardinal characteristics which describe part of the combinatorial structure of . We provide various consistency results; e.g. we show how to force simultaneously many characters and many -characters. We also investigate two ideals on the Baire space naturally related to and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.

     

Generalized fuzzy ideals of near-rings

The concept of（∈,∈∨q）-fuzzy subnear-rings（ideals） of a near-ring is introduced and some of its related properties are investigated.In particular,the relationships among ordinary fuzzy subnear-rings（ideals）,（∈,∈∨ q）-fuzzy subnear-rings（ideals） and（∈,∈∨q）-fuzzy subnear-rings（ideals） of near-rings are described.Finally,some characterization of [μ]t is given by means of（∈,∈∨ q）-fuzzy ideals.     

U-factorization of ideals

We study the factorization of ideals of a commutative ring, in the context of the U-factorization framework introduced by Fletcher. This leads to several “U-factorability” properties weaker than unique U-factorization. We characterize these notions, determine the implications between them, and give several examples to illustrate the differences. For example, we show that a ring is a general ZPI-ring if and only if its monoid of ideals has unique factorization in the sense of Fletcher. We also examine how these “U-factorability” properties behave with respect to several ring-theoretic constructions.     

Powers of edge ideals with linear resolutions

We show that if G is a gap-free and diamond-free graph, then I(G)^s has a linear minimal free resolution for every s≥2.     

Geometric interpretation of tight closure and test ideals

We study tight closure and test ideals in rings of characteristic using resolution of singularities. The notions of -rational and -regular rings are defined via tight closure, and they are known to correspond with rational and log terminal singularities, respectively. In this paper, we reformulate this correspondence by means of the notion of the test ideal, and generalize it to wider classes of singularities. The test ideal is the annihilator of the tight closure relations and plays a crucial role in the tight closure theory. It is proved that, in a normal -Gorenstein ring of characteristic , the test ideal is equal to so-called the multiplier ideal, which is an important ideal in algebraic geometry. This is proved in more general form, and to do this we study the behavior of the test ideal and the tight closure of the zero submodule in certain local cohomology modules under cyclic covering. We reinterpret the results also for graded rings.

     

A note on the critical ideals of a cycle

Critical ideals of a graph G which are the determinantal ideals of its generalized Laplacian matrix were first introduced by Corrales and Valencia as a generalization of the critical group. Then it was shown that critical ideals are also closely related to other properties of the graph, such as the clique number and the zero forcing number. In this note, we give a simple proof of Theorem 4.13 proved in [7], which gives a Gröbner basis of the first nontrivial critical ideal of a cycle. After that as applications we determine explicit expressions for the characteristic ideals of a cycle and the critical groups of a family of thick wheels.