Artin局部主理想环上多项式理想的Grobner基的标准型

本文给出Artin局部主理想环上单变元多项式理想的极小Gr     

A Nonlinear Version of Noether's Type Theorem

Abstract

Let L be a line bundle on a smooth curve C, which defines a birational morphism onto Φ(C) ? P ^r . We prove that, under suitable assumptions on L, which are satisfied by Castelnuovo's curves, a generic section in H ⁰(C, L ²) can be written as α² + β² + γ², with α, β, γ ∈ H ⁰(C, L). If there are no quadrics of rank 3 containing Φ(C), this is true for any section. For canonical curves, this gives a non linear version of Noether's Theorem.     

半群的次极大理想与次极小理想

在半群中引入次极大理想和次极小理想的概念，研究了它们的基本性质．证明了次极大理想的存在性，并得到如下定理，半群中每个理想可以分解成一些次极大理想的交，特别地，在满足理想降链条件的半群中，每个理想可以分解成有限个次极大理想的交，对于次极小理想．可以得到对偶的结果．     

环的次极大理想

引入了环的次极大理想的概念,讨论了它的性质,并得到比环的理想的准素分解定理更普遍的结论。     

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。     

理想簇和根理想

关于环的理想的根有两种定义,一种是所有包含I的极大理想的交,另一种是所有包含I的素理想交,本文主要研究后者定义的一些性质,以及和理想簇V(I)(所有包含I的素理想的集合)的关系.     

关于循环环的理想、素理想和极大理想

研究了循环环R=的理想、素理想和极大理想的个数和结构,得到了如下结论:1)理想:（1）若|R|=∞,则R共有无穷多个理想:;（2）若|R|=n,设n的正因数个数为T（n）,则R共有T（n）个理想:.2)素理想:（1）若|R|=∞,设a²=ka（k≥0）,①当k=0时,R的素理想只有R;②当k>0时,R的素理想共有无穷多个,它们是:{0}、R及;（2）若|R|=n>1,设a²=ka,0≤k.3）极大理想:（1）若|R|=∞,则R有无限多个极大理想,它们是;（2）若|R|=n>1,设n的互不相同的素因数个数为ψ（n）,则R共有ψ（n）个极大理想:(pa|p是n的素因数>.     

Canonical correlations in multi-way layout

In this paper, some formulas are proposed, which concern the numbers of unit canonical correlations in a multi-way layout. Different types of canonical correlations are considered and their connection with connectedness and orthogonality are examined.     

Full Ideals

Contractedness of 𝔪-primary integrally closed ideals played a central role in the development of Zariski's theory of integrally closed ideals in two-dimensional regular local rings (R, 𝔪). In such rings, the contracted 𝔪-primary ideals are known to be characterized by the property that I: 𝔪 = I: x for some x ∈ 𝔪 ?𝔪². We call the ideals with this property full ideals and compare this class of ideals with the classes of 𝔪-full ideals, basically full ideals, and contracted ideals in higher dimensional regular local rings. The 𝔪-full ideals are easily seen to be full. In this article, we find a sufficient condition for a full ideal to be 𝔪-full. We also show the equivalence of the properties full, 𝔪-full, contracted, integrally closed, and normal, for the class of parameter ideals. We then find a sufficient condition for a basically full parameter ideal to be full.     

Banach spaces of operators that are complemented in their biduals

Let [A, a] be a normed operator ideal. We say that [A, a] is boundedly weak*-closed if the following property holds: for all Banach spaces X and Y, if T: X → Y** is an operator such that there exists a bounded net (T _i ) _i∈I in A(X, Y) satisfying lim _i 〈y*, T _i x y*〉 for every x ∈ X and y* ∈ Y*, then T belongs to A(X, Y**). Our main result proves that, when [A, a] is a normed operator ideal with that property, A(X, Y) is complemented in its bidual if and only if there exists a continuous projection from Y** onto Y, regardless of the Banach space X. We also have proved that maximal normed operator ideals are boundedly weak*-closed but, in general, both concepts are different.      

BCK-代数的极小理想与次极小理想

在BCK-代数中,引入了极小理想与次极小理想的概念,研究了极小与次极小理想的若干性质,它们同文[5]、文[6]中的有关概念与结果是对偶的.     

关于典范体积形式的一个公式

本文给出了一个典范体积（Canonical volume)形式公式的代数证明。     

Fuzzy格的M-理想

Ｍ－理想是Ｆｕｚｚｙ格的特有概念,在Ｆｕｚｚｙ格的研究中,有它的独特优势。本文首先给出Ｍ－理想的一般性质;其次给出了Ｍ－理想与同余关系及同态的对应关系;最后,给出了Ｍ－理想并的新的构造等式,证明了当主Ｍ－理想完备时,Ｆｕｚｚｙ格的全体主Ｍ－理想构成完备分配格     

理想单子在非标准饱和模型下的若干应用

通过利用非标准分析中的饱和模型,对其中的理想进行了讨论,从而得到了理想的非标准特征,并进一步利用这一特征证明了单子论中的一些相关定理．