局部左正则纯正密群的一个等式

本文给出局部左正则纯正密群的一个等式.证明了一个完全正则半群是左半正规密群当且仅当它是局部左正则纯正密群.     

P-完全正则半群

求证具有强半格结构的完全正则半群成为P-完全正则半群的充分条件.利用半群的强半格结构以及同余的性质.完全单半群的强半格-正规群带是P-完全正则半群.矩形群的强半格正规纯正群类ONBG,左群的强半格左正规纯整群类LONBG,群的强半格Clifford半群类,矩形带的强半格正规带类NB,都具有性质P.     

正规纯正左消幺半群并半群上的(*,~)-好同余(英文)

本文利用(*,~)-好同余对刻画了正规纯正左消幺半群并半群上的(*,~)-好同余.此结果将正则半群中有关正规纯正群并半群上同余的相关结论推广到了r-wide半群中.     

LR-正规纯正群并半群

引进和研究了一类新的正则纯正群并半群, 即LR-正规纯正群并半群. 特别地,在构作LR- 正规纯正群并半群中引进了啮合技术来处理强半格中的半群分量.     

乘法半群为左正规纯正群的半环

研究了加法半群为半格,乘法半群为左正规纯正群的半环．证明了此类半环（S,＋,．）可以嵌入到半格（S,＋）的自同态半环中．构造S的一个特定的偏序关系,得到了（S,·）上的自然偏序与所构造偏序相等的等价条件．     

具有Clifford断面的正则纯正半群

给出了具有Clifford断面的右正规纯正半群的等价刻画,得到了具有Clifford断面的正则纯正半群的次直积分解,证明了具有Clifford断面的正则纯正半群一定是正则纯正群．     

纯正半群上的强同余及Clifford同余

把Reilly对逆半群的幂等元集合的正规划分的概念推广到纯正半群,用它从另一角度刻画。了纯正半群上强同余的结构.并刻画了具有T关系的两个强同余的联和交的正则核正规系,又讨论了纯正半群上的Clifford同余,给出了最小Clifford同余的刻画.     

具有左中心幂等元的弱L-正则半群

本文证明了半群S是一个具有左中心幂等元的弱L-正则半群,当且仅当S为H-左可消幺半群和右零带直积的强半格,并借助具有中心幂等元的弱L-正则半群和右正规带建立了半群S的强织积结构.     

纯正半群上的同余扩张(二)

刻画半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题（参见［1－5］）本文在[6]讨论了带上的同余的正规性和不变性以及在其Hall半群上的扩张的基础上,从同余扩张的角度刻划了完全正则的纯正半群的特征（定理26）,给出了一个纯正半群的带上的所有同余都可以扩张到这个纯正半群的充分必要条件．     

强双单严格纯正半群上同余的刻划

本文利用正则半群同余的概念，找到了任一强双单严格纯正半群Ｓ的一个正规子半群ＮＫ和Ｅ上的一个正规同余ГＰ，证明了Ｓ的任何一同余可由余偶确定，从而给出了Ｓ上任一同余的一个具体刻划。     

Orthodox semigroups whose idempotents satisfy a certain identity

An orthodox semigroup S is called a left [right] inverse semigroup if the set of idempotents of S satisfies the identity xyx=xy [xyx=yx]. Bisimple left [right] inverse semigroups have been studied by Venkatesan [6]. In this paper, we clarify the structure of general left [right] inverse semigroups. Further, we also investigate the structure of orthodox semigroups whose idempotents satisfy the identity xyxzx=xyzx. In particular, it is shown that the set of idempotents of an orthodox semigroup S satisfies xyxzx=xyzx if and only if S is isomorphic to a subdirect product of a left inverse semigroup and a right inverse semigroup.     

具有逆断面的正规纯正半群

A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band.We deal with congruces on a normal orthodox semigroup with an iverse transversal .A structure theorem for such semigroup is obtained.Munn(1966)gave a fundamental inverse semigroup Following Munn‘s idea ,we give a fundamental normal orthodox semigroup with an inverse transversal.     

A note on maximal subgroups of free idempotent generated semigroups over bands

We prove that all maximal subgroups of the free idempotent generated semigroup over a band B are free for all B belonging to a band variety V if and only if V consists either of left seminormal bands, or of right seminormal bands.     

Semilattices of bisimple orthodox semigroups

A structure theorem for bisimple orthodox semigroups was given by Clifford [2]. In this paper we determine all homomorphisms of a certain type from one bisimple orthodox semigroup into another, and apply the results to give a structure theorem for any semilattice of bisimple orthodox semigroups with identity in which the set of identity elements forms a subsemigroup. A special case of these results is indicated for bisimple left unipotent semigroups.     

Congruences on regular semigroups

The kernel of a congruence on a regular semigroup S may be characterized as a set of subsets of S which satisfy the Teissier-Vagner-Preston conditions. A simple construction of the unique congruence associated with such a set is obtained. A more useful characterization of the kernel of a congruence on an orthodox semigroup (a regular semigroup whose idempotents form a subsemigroup) is provided, and the minimal group congruence on an orthodox semigroup is determined.     

半群上的模糊群同余

设 S是一个半群 ,ρ是 S上的一个模糊同余。引进半群的模糊半正规子半群的概念 ,证明ρ是 S上的一个模糊群同余当且仅当它的模糊核 K(ρ)是 S的模糊半正规子半群 ;而且对每个给定的模糊半正规子半群 μ可以构造一个模糊同余 ρμ 使得它的模糊核 K(ρμ) =μ.     

右逆半群上的偏序关系

It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a fight inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y.     

E-unitary almost factorizable orthodox semigroups

It is established that an E-unitary almost factorizable orthodox semigroup need not be isomorphic to a semidirect product of a band by a group, and a necessary and sufficient condition is given for an E-unitary almost factorizable orthodox semigroup to be isomorphic to such a semidirect product. Moreover, the structure of every E-unitary almost factorizable orthodox semigroup is described by means of bands and groups.