幺半群的半直积及其同余

给出了两个幺半群的半直积是Ｃｌｉｆｆｏｒｄ半群的充要条件及其结构。并讨论了逆半群半直积的Ｇｒｅｅｎ关系、最小群同余和极大幂等元分离同余。     

含幺逆半群的半格的同余对

本文利用一族含幺逆半群的同余对刻画了其半格的同余对,并给出了含幺逆半群半格的正规同余对族的格与其标准同余对的格之间的同构关系.     

含幺Clifford半群上的Rees矩阵半群的同余和正规加密群结构

给出了含幺Clifford半群上的Rees矩阵半群S的正规加密群结构,证明了在含幺Clifford半群上的Rees矩阵半群S上以下两个条件是等价的:(1)S上的同余ρ是完全单半群同余;(2)S上的同余ρ和S上的相容组之间存在保序双射.最后还证明了S上的完全单半群同余所构成的同余格是半模的.     

半群的半直积及其同余

给出了两个幺半群的半直积是Ｃｌｉｆｏｒｄ半群的充要条件及其结构．并讨论了逆半群半直积的Ｇｒｅｅｎ关系、最小群同余和极大幂等元分离同余．     

纯正半群上的同余扩张(一)

刻划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．本文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，从同余扩张的角度刻划了带上的同余的性质，给出了扩张的极大、极小同余的描述．     

含幺逆半群的半格上的同余格

本文证明了含幺逆半群Sα（α∈Y）的半格的容许同余格同构于半格S上同余格的一个子格。     

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.     

具有逆断面的正则半群的同余的表示

具有道断面S°的正则半群可表示为有Saito's结构的半群W（I，S°，Λ，*，α，β）.我们利用由I，S°和Λ上的同余构成的所谓同余聚抽象地表示这类半群上的同余，进而给出了这类半群的同态象的构造法．     

Γ—正则半群上的若干同余

本文首先给出了Γ－正则半群上的群同余刻划。然后定义了Γ－逆半群的幂等分离核正规系，证明了Γ－逆半群上的幂等分离核正规系决定一个Γ－逆半群上的等分离同余，及Γ－逆半群上的幂等分离同余核是一个等分离核正规系。     

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。     

右（左）逆半群的半直积及圈积

给出了两个幺半群的半直积及圈积为右（左）逆半群的充分必要条件，从而推广了[2]中两个幺半群的半幺直积和圈积为逆半群的充分必要条件．     

半群半直积的主投影性质(英文)

本文研究了半群半直积的主投影性质.利用适当半群,获得了右主投影半群半直积的充分和必要条件,推广了半直积的一些结果.     

Some Ideal Lattices in Partial Abelian Monoids and Effect Algebras

Congruences and ideals in partial Abelian monoids (PAM) are studied. It is shown that the so-called R ₁-ideals in cancellative PAMs (CPAM) form a complete Brouwerian sublattice of the lattice of all ideals, and they are standard elements of it. In a special class of CPAMs, effect algebras, properties of ideals and congruences are studied in relation to the generalized Sasaki projections and dimensional equivalence.     

A delay theorem for pointlikes

This paper shows that, for a pseudovariety V of monoids, V * D has decidable pointlikes if and only if V does. In the process, we develop a theory of pointlike sets for categories and a generalization of the Derived Category Theorem to understand how pointlike sets behave with respect to the semidirect product. This paper is intended to be the first of two papers concerning algorithmic problems for semidirect products of pseudovarieties.     

C-rpp半群的半直积

给出了两个幺半群的半直积是C-rpp半群的充要条件及结构。     

弱Clifford拟正则半群的半直积和圈积

本文给出两个么半群Ｓ和Ｔ的半直积和圈积为弱Ｃｌｉｆｆｏｒｄ拟正则么半群的充要条件和半直积的结构，同时还讨论了弱Ｃｌｉｆｆｏｒｄ拟正则么半群的最小群同余与半直积的最小群同余之间的关系．     

Tied monoids

We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting on monoids of set partitions. The nature of our monoids indicate that they should give origin to new knot algebras; indeed, our tied monoids include the tied braid monoid and the tied singular braid monoid, which were used, respectively, to construct new polynomial invariants for classical links and singular links. Consequently, we provide a mechanism to attach an algebra to each tied monoid; this mechanism not only captures known generalizations of the bt-algebra, but also produces possible new knot algebras. To build the tied monoids it is necessary to have presentations of set partition monoids of types A, B and D, among others. For type A we use a presentation due to FitzGerald and for the other type it was necessary to built them.

     

Semidirect products and wreath products of strongly π-inverse monoids

In this paper we determine the necessary and sufficient conditions for the semidirect products and the wreath products of two monoids to be strongly -inverse. Furthermore, we determine the least group congruence on a strongly -inverse monoid, and we give some important isomorphism theorems.     

左中心rpp半群的半直积

讨论了幂等元都是左中心元的rpp半群的半直积,给出了这种半群半直积的充要条件,推广了一些已知的结果.