發(fā)布時間：2018-04-18 23:39

  本文選題：雙循環(huán)半群 + 格�。� 參考：《西北大學》2015年碩士論文

【摘要】：雙循環(huán)半群是一類特殊的逆半群.本文從雙循環(huán)半群上的同余關系出發(fā),對雙循環(huán)半群的結構與性質給出了具體描述.主要結果如下：1.從雙循環(huán)半群上的一類同余出發(fā),討論了冪等元所在的同余類,證明了這樣的同余類是逆半群,進而給出了雙循環(huán)半群上任一同余的冪等元同余類是正則半群的結論.2.從雙循環(huán)半群上的同余關系出發(fā),討論了雙循環(huán)半群關于這類同余的交做成的商群,且對這種商群的具體元素進行了刻畫,給出了雙循環(huán)半群到整數(shù)加法半群的同態(tài)映射,目的為了探討雙循環(huán)半群上的同態(tài)核,結果證明了雙循環(huán)半群上的同態(tài)核是最小群同余,得到了這類特殊同余的交也是最小群同余的結論.3.從雙循環(huán)半群上的同余關系出發(fā),證明了雙循環(huán)半群上的一類同余ρd(d ∈ N)與其逆子半群之間的相互唯一確定關系,并對這種同余做成的集合以及逆子半群做成的集合進行了刻畫,證明了這種同余做成的格與自然數(shù)集在某種偏序下做成的格同構,接著對雙循環(huán)半群上與Green關系有關的問題作進一步探究,得到了與之有關的結論.
[Abstract]:A bicyclic semigroup is a special inverse semigroup.Based on the congruence relation on bicyclic Semigroups, the structure and properties of bicyclic Semigroups are described in detail in this paper.The main results are as follows: 1.Starting from a class of congruences on a bicyclic semigroup, this paper discusses the congruence classes of idempotent elements, proves that such congruences are inverse Semigroups, and then gives the conclusion that the idempotent congruences of bicyclic Semigroups are regular Semigroups.Based on the congruence relation on bicyclic Semigroups, this paper discusses the quotient groups formed by the intersection of this class of congruences, and characterizes the specific elements of this quotient group, and gives the homomorphic maps from bicyclic Semigroups to integer additive Semigroups.Aim in order to study homomorphic kernels on bicyclic Semigroups, we prove that homomorphic kernels on bicyclic Semigroups are minimal group congruences, and obtain the conclusion that the intersection of such special congruences is also a minimal group congruence.Based on the congruence relation on a bicyclic semigroup, this paper proves the mutual unique definite relation between a class of congruence 蟻 DU d 鈭，

本文編號：1770629