The monoid can be found in many branches of mathematics.

独异点在许多的数学分支中都会出现。

Monoids are often used as a solid algebraic basis for computer science.

幺半群常被用来当做计算机科学的坚固代数基础。

Some important results in the study of monoids are Crohn Rhodes theorem and star height problem.

幺半群的研究中一些较重要的结论有克罗恩-罗德斯定理和星高问题。

Bipartite graphs with P-regular endomorphism monoids are characterized. P-regularity of the endomorphism monoid of lexicographic product of graphs is discussed.

刻划了具有P -正则自同态幺半群的二分图，讨论了字典序积图的自同态幺半群的P -正则性。

In this article, we showed the algebraic structure of syntactic categories based on monoid and defined categorial equation whose solutions are described by consistency and correlation .

本文给出了建立在含幺半群基础上的范畴语法的代数结构 ，定义了范畴方程和它的解并对范畴方程的解作了分类 ：相容性的相关性。

This paper has firstly defined the factor struture M/P(M) of commutatiuely residual monoid M by its sub-monoid P(M), then we have studied its properties and given out some isomorphism theorem.

本文首先定义了交换剩余幺半群M相对于其子半群P（M）的商结构M／P（M），然后研究了它的性质并给出了一些同构定理。

In this paper, we propose a reduced linear representation of such distribution based on the formal power series on free monoid which can be easily used to calculate the probability distribution.

该文利用自由幺半群上的有理形式幂级数理论，构造出该概率分布的约化线性表示，从而完全解决了噪声变量的概率分布计算问题。