It is obtained that the commutative completely idempotent algebra which has unit element and no zero factor is a extension field on F. The structure of two dimension completely idempotent algebra is given out.

We present the trigonometric representations of structured matrices by using displacement rank and commutative Hessenberg matrix algebra. Applications on Toeplitz and Toeplitz-plus-Hankel matrices are discussed.

利用位移秩和交换Hessenberg矩阵代数给出结构矩阵的三角表示，并讨论在Toeplitz矩阵和Toeplitz+Hankel矩阵方面的应用。

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Some theorems of density in strong commutative subspace lattice algebra are given.

给出了强交换子空间格（S－CSL）代数中的几个稠密性定理。

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Rules can also be used for commutative and noncommutative algebra.

规则可以用于交换和非交换代数。

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In this paper we discuss some properties of M ( A), the multiplier algebra of a commutative BANACH algebra A, and obtain the following result: If A is a faithful commutative-algebra, then so is M ( A).

本文讨论了交换Banach代数A的乘子代数（A）的若干性质，并且得到了如下的结论：如果A是一个忠实交换的~代数，那么M（A）也是一个交换的~代数。

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The realization theory of linear systems defined over a commutative Banach algebra W is studied. For the given strictly proper rational matrix function over W, using the matrix fraction description, the controllable and observable realizations have been constructed.

研究变换Banach代数W上线性系统的实现理论，对给定的W上的严格真有理矩阵函数，利用其矩阵分式描述，构造了其可控形和可观测形的实现；

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In this paper, we shall introduce the concept of discrete BCK algebra, and discuss its relation with BCK-algebra generated by atoms, positive implicative BCK-algebra, commutative BCK algebra and its self algebraic properties.

本文引入离散型BCK代数概念，并探讨它与原子生成的BCK代数、正关联BCK代数、交换BCK代数之间的关系及其自身的一些代数性质。

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In this paper, the Riemann-Hilbert boundary value problem for a class of first order hyperbolic equation in commutative quaternion algebra is considered, and the general solutions and the solvable conditions of the problem in different cases are obtained.

讨论了可换四元数代数中一类一阶双曲方程的Riemann-Hilbert边值问题.获得了其解的一般形式，以及在不同情况下Riemann-Hilbert边值问题的可解条件。

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The main results are: Each Commutative FI algebra can be embedded into direct product of a system of linearly ordered Commutative FI algebra s;

主要结果是：交换FI代数可同构嵌入一族全序交换FI代数的直积；

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Let H be a finite dimensional Hopf algebra and A a commutative H-module algebra.

设H是有限维Hopf代数，A是交换的H-模代数。

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The spectral extension property of commutative Banach algebra

交换Banach代数的谱延拓性质

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The Riemann-Hilbert Boundary Value Problem for a First Order Hyperbolic Equation in Commutative Quaternion Algebra

可换四元数代数中一类一阶双曲方程的Riemann-Hilbert边值问题

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Equivalent conditions for reducible elements of a complex commutative Banach algebra

复交换Banach代数中可约元的等价条件

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Discontinuous Characteristic Boundary Value Problems for Hyperbolic Equations in Commutative Quaternion Algebra

交换四元数代数中一类双曲型方程的间断特征边值

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Realization theory of linear systems defined over a commutative Banach algebra

交换Banach代数上线性系统的实现

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For commutative algebra, algebraic geometry, and singularity theory, the SINGULAR computer algebra system provides a large variety of algorithms in the package kernel as well as shared libraries.

对于交换代数、代数几何和奇点理论，SINGULAR计算机代数系统在软件包内核以及共享库中提供了大量的算法。

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CFSTI ( Clearinghouse for Federal Scientific and Technical Information) The central notion in commutative algebra is that of a prime ideal.

交换代数中最核心的概念就是素理想。

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Computations in Commutative Algebra ( CoCoA) is another free computer algebra system for working with very large integers, rational numbers, and polynomials.

Computations in Commutative Algebra（CoCoA）是另一个免费计算机代数系统，用于处理超大型整数、有理数和多项式。

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Homological Dimension of Quantum Commutative Algebra

量子交换代数的整体同调维数

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The theory of modules is increasingly important in modern mathematics. It unifies many mathematical structures, and is the basic tools in commutative algebra.

模的理论是现代数学中越来越重要的工具，它统一了许多数学结构，也是研究交换代数的基本工具。

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Method of localization is a important tool in Commutative Algebra. The whole properties are always obtained by studying local properties of Algebraic Variety.

局部化（Localization）方法是交换代数中一个重要工具，通过研究一个代数簇（AlgebraicVariety）在某点或某点附近的局部性质，往往可以把握代数簇的整体特性。

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