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.
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.
利用群核正规系讨论了纯正群的幂等元分离同余。
Then we study the idempotent-separating congruences on the orthogroups with group kernel normal systems and give it a simple rep.
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.
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.
幂等元与本原幂等元在环中有非常重要的地位与作用。
Idempotents and primitive idempotents have very important station in the ring.
如果它是有限和非空的，则它必须包含至少一个幂等元。
If it is finite and nonempty, then it must contain at least one idempotent.
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.
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.
每个子群精确的包含一个幂等元，也就是这个子群的单位元。
Each subgroup contains exactly one idempotent, namely the identity element of the subgroup.
设R是一阿贝尔环（R的所有幂等元都在中心里），A是R上的一幂等阵。
Let R be an abelian ring ( all idempotents of R lie in the center of R), and A be an idempotent matrix over R.
本文证明在类空间存在一生成基，与投影算符或幂等元相反，它是各次幂不等的。
In this paper we showed that there is a generating basis in class space. It differs from the projection operators and idempotent for every power which is not equal to itself.
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.
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.
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.
本文研究在一个有单位元的环中两个倍幂等元的换位子与两个倍对合元的换位子的可逆性问题。
This paper is a study on the invertibility of the commutator of scalar-idempotent elements and scalar-involutory elements of a unitary ring.
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.
当有限域的特征不整除群的阶时，给出了直接写出相应的多项式环的本原幂等元的方法，从而可以直接写出所有的极小循环码。
In the case of(Char(F_q), |G|)=1, we provide a method that writing down directly all the primitive idempotents of related polynomial ring, and hence that of all the minimum cyclic codes.
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.
得到了既约剩余系中同阶元的等幂和的一系列性质及其计算公式，并给出了证明。
This article has obtained a series properties and a calculate formula of the sum of the equal powers of the elements of the same order in the reduced residue system.
得到了既约剩余系中同阶元的等幂和的一系列性质及其计算公式，并给出了证明。
This article gives a property and a corollary which is like Chowla s theorem, for reduced residue system.
得到了既约剩余系中同阶元的等幂和的一系列性质及其计算公式，并给出了证明。
This paper considers some properties of the sum of equal powers and the product of the elements of the same order in the reduced residue system.
得到了既约剩余系中同阶元的等幂和的一系列性质及其计算公式，并给出了证明。
This paper considers some properties of the sum of equal powers and the product of the elements of the same order in the reduced residue system.
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