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1·The number of polynomial function over a finite commutative ring.

有限交换环上的多项式函数的个数问题。

2·As the main results, it gives a Positivstellensatz, a Nullstellensatz and a Nichtnegativstellensatz for matrices over a commutative ring.

作为本文的主要结果，关于交换环上矩阵的正点定理，零点定理和非负点定理被建立。

3·On commutative ring with the identity, the definition of affine Lie algebras was given by applying the means of generator and defining relation.

在有单位元的交换环上，可应用生成元和定义关系的方法给出仿型李代数的定义。

4·In this paper, we introduce the notion of M-valuation systems for a commutative ring, and investigate the M-valuations from the inside of a commutative ring.

在本文中，我们引进了M -赋值系统的概念，从环的内部给出交换环上M -赋值的结构。

5·The commutative problem of arbitrary PI ring is the main research contents of the commutative theory.

任意pi -环的交换性问题是环的交换性理论的一个主要内容。

6·This paper mainly discuss some property of ring which fit into anti-commutative law, and arrive at a conclusion that anti-commutative law is commutable.

本文主要讨论了适合反交换律的环的一些性质，并得出反交换环一定是交换环。

7·The commutative theorem characterized by an associative ring, presented in document 1 noted by Guo Huaguang is extended to the formation of the left near ring with partition law.

把郭华光在文献[1]中关于结合环的交换性定理推广到分配生成左拟环上。

8·The fractional ring(module)and the interrelated localization method are the important tools for commutative algebra.

分式环和分式模以及与之相关的局部化方法是交换代数中一个重要工具。