1) The smallest right zero semigroup congruence
最小右零半群同余
2) The minimum inverse semigroup congruence
最小逆半群同余
3) the minimum regular *-semigroup congruence
最小正则*-半群同余
1.
The aim of this paper is to study the minimum regular *-semigroup congruence on strongly P-regular semigroup S(P) ,which can also be written as simplify form γP when we take advantage of the regular*-transversal S° of S(P) .
主要研究了强P-正则半群S(P)上的最小正则*-半群同余。
4) least group congruence
最小群同余
1.
We give a relation R on a π-regular semigroup S described as: R={(aea m-1a 1f,(aea m-1a 1f)2)∈S×S,am∈RegS,a 1∈V(am),e,f∈E(S)} ∪{(vb n-1b 1ub,(vb n-1b 1μb)2)∈S×S|b∈RegS,b 1∈V(bn),μ,v∈E(S)} and the least group congruence ρ# generated by R.
在π -正则半群S中 ,给出了关系R={(aeam- 1 a1 f,(aeam- 1 a1 f) 2 ) ∈S×S|a∈S ,am ∈RegS ,a1 ∈V(am) ,e ,f∈E(S) }和由R生成的最小同余ρ#,给出了S的最小群同余的刻划 。
5) the minimum group congruence
最小群同余
1.
in this paper, and the minimum group congruence on the semigroups is obtained.
定义了严格π-正则半群上的群同余,并给出了该类半群上的最小群同余的刻画。
2.
For e, f∈E(S), if there exists m∈N such that(efe)m = (ef)m (efe)m = (fe)m ),we prove that the following binary relations: {(a,b)∈S×S:ea=eb for some e∈E (S) } (σ={(a,b)∈S×S:ae=be for some e∈E(S) } are the minimum group congruences on S.
证明了如果拟正则半群S的幂等元集E(S)满足以下条件:对任意的e,f∈E(S),存在m∈N,使得(efe)m=(ef)m((efe)m=(fe)m),则σ1={(a,b)∈S×S|e∈E(S),使得ea=eb}(σ2={(a,b)∈S×S|e∈E(S),使得ae=be})是S的最小群同余。
6) the least group congruence
最小群同余
1.
Furthermore,the least group congruence and the maximum idempotent-separating congruence on the semidirect products of right groups are discussed.
从右群的另一定义出发给出了两个半群的半直积和圈积是右群的充分必要条件,并讨论了右群的半直积的最小群同余和最大幂等分离同余。
2.
A new kind of semigroup,left(right) strongly π-inverse semigroup is defined,the least group congruence on a left(right) strongly πinverse semigroup is characterized by method of the idempotents means.
定义了一种新的左(右)强π-逆半群,利用幂等元方法给出了左(右)强π-逆半群的一个最小群同余。
3.
From this,the least group congruence on a π-inverse semigroup is given.
由此可得π-逆半群的最小群同余。
补充资料:幂零半群
幂零半群
ralpotent semi-group
幂零半群[司脚触吐涨”‘一沙叨p;。,二‘noTeoT皿明。o几犷-pyn“a] 具有零元的半群(~一脚uP)S,且存在n使得罗=0.这等价于S中的恒等式 xl”‘x。二yl‘’‘y。·对于给定的半群,满足上述性质的最小的n称为幂零级(stePof司potency)或幂零类(cla义of汕potency).如果S’=O,则S称为具有零乘法的半群(se而一groupwith~甘山拓pliCa石on).下列关于半群S的条件等价:1)S是幂零的;2)5有一个有限零化子序列(即一个有限长度的升零化子序列,见诣零半群(nil semi一grouP));3)存在k使得S的每个子半群都可作为一个长度(k的理想序列被嵌人. 更为广泛的概念是Ma月H那B意义下的幂零半群(【2』).该名称指这样的半群,对于某个。,它满足恒等式 戈,Y。,其中字戈和Y。归纳地定义如下:X0=x,Y。=y,戈=戈一:u,Y。一,Y。=欢_lu。Xn_,,这里x,夕和“。,…,“。全是变量.一个群是Ma月玉u”B意义下的幂零半群,当且仅当它在通常群论意义下是幂零的(见幕零群(面训七以gro叩)),而恒等式戈=玖等价于这样的事实:该群的幕零类簇n.满足等式戈二Y。的消去半群可嵌人到一个满足同样等式的群中.
说明:补充资料仅用于学习参考,请勿用于其它任何用途。
参考词条