运行这段代码确保可以求幂（忽略我之前提到的bug），这样就完成了一半的工作。
Running this code verifies that exponentiation works (modulo the bug I mentioned earlier), so half of the battle is now complete.
刻划了S-正则半群上的极大幂等元分离同余并给每个S-正则半群一个基本表示。
The maximum idempotent - separating congruence on a S - semigroup is characterized and a fundamental representation of a such semigroup is given.
左半正规纯正半群是幂等元集形成左半正规带的纯正半群。
A left seminormal orthodox semigroup is an orthodox semigroup whose idempotents form a left seminormal band.
一个有限半群是满足左正则性条件的IC富足半群当且仅当它是一个幂等元形成左正则带的纯整超富足半群，但满足左正则性条件的无限IC富足半群不都是幂等元形成左正则带的纯整超富足半群。
A finite semigroup is an IC abundant semigroup satisfying the left rgularity condition if and only if it is an orthodox superabundant semigroup whose idempotents form a left regular band.
给出了布尔群代数半群中的幂等元、极大子群和正则元的结构以及幂等元和正则元的个数。
The structure of the idempotent elements, regular elements and maximal subgroups and the number of the idempotent elements and regular elements in Boolean group algebra are given.
首先在正规子群与同余的关系的基础上，采用类比的方法，从同余的角度给出了群的正规列幂半群的另一种刻画。
In this paper, based on the relation between normal subgroup and congruence, another depiction of normal series power semigroup is given from the angles of congruence by the method of analogy.
在给出它的若干特征之后，指出这一类半群也是群的矩阵的幂零元-理想扩张，但反之未必成立。
Also, after some prelimenaries, We have Obtained that the semigroup is further nil-extension of the matrix of groups, but the converse is not all true.
正则半群上的同余是由其幂等元同余类所完全决定的。
The congruences on a regular semigroup is completely determined by its idempotent congruence classes.
其次，对这类半群上的群同余、最小群同余、正则同余、幂等分离同余做了进一步研究。
Then group congruences, the least group congruence, regular congruence, and idempotent-seperating congruence on such semigroups are obtained.
本文证明了纯正么半群在其幂等元带上的局部化存在唯一，且证明了它是其最大群同态象。
This paper proves that the localization of an orthodox semigroup at the semilattice of idempotences exists and is unique which is the maximum group homomorphism image.
由此推出了P -正则半群上的每个P -同余完全是由其包含幂等元的部分核正规系所决定的。
So We have prove that each P-congruence on P-regular semigroups is uniquely determined by its partial kernel normal systems containing idempotent elements.
本文主要研究加法幂等元满足置换等式的纯整半环。
This paper deals with orthodox semirings whose additive idempotents satisfy permutation identities.
介绍弱左正则幺半群的概念，指出在可交换半群中，完全正则、弱左(右)正则和完全幂等是等价的。
In this paper, we introduce the notion of left weakly regular semigroup and show that in a commutative semigroup, the complete regularity, regularity, left resp.
本文定义了有核半群的局部幂零根，并证明了与环相近的一些性质。
In this paper, we define the local nilpotent radical of a semigroup having kernel and prove some properties which is similar to rings.
目的研究一类重要的幂等元半环，即乘法带半环。
Aim To study a very important class of idempotent semiring, so-called multiplicative band semirings.
讨论一类可数离散半群上概率测度卷积幂的弱收敛性，主要结果是利用局部群化的观点给出了概率测度卷积幂弱收敛的一个充分条件。
The main result is that we get a sufficient condition for the weak convergence of convolution powers of probability measures, by using the method of local grouplization.
刻画了弱逆半群s上的最大幂等元分离同余和最小群同余。
In this paper, the greatest idempotent separating congruence and the minimum group congruence on a weakly inverse semigroup s are characterized.
目的研究幂等元半环簇的重要子簇（?）。
Aim To study the important subvarieties (?) M and (?) M of the variety of idempotent semirings.
给出了幂半群的概念，研究了幂半群的同态与同余关系，讨论了它们之间的关系，并得到了一些理想的结果。
It introduces the concept of power semigroup, studies the relations between homomorphism and congruence of power semigroup and obtains some perfect results.
给出了幂半群的概念，研究了幂半群的同态与同余关系，讨论了它们之间的关系，并得到了一些理想的结果。
It introduces the concept of power semigroup, studies the relations between homomorphism and congruence of power semigroup and obtains some perfect results.
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