双循环半群上的同余关系

发布时间：2018-04-18 23:39

  本文选题：双循环半群 + 格　； 参考：《西北大学》2015年硕士论文

【摘要】：双循环半群是一类特殊的逆半群.本文从双循环半群上的同余关系出发,对双循环半群的结构与性质给出了具体描述.主要结果如下：1.从双循环半群上的一类同余出发,讨论了幂等元所在的同余类,证明了这样的同余类是逆半群,进而给出了双循环半群上任一同余的幂等元同余类是正则半群的结论.2.从双循环半群上的同余关系出发,讨论了双循环半群关于这类同余的交做成的商群,且对这种商群的具体元素进行了刻画,给出了双循环半群到整数加法半群的同态映射,目的为了探讨双循环半群上的同态核,结果证明了双循环半群上的同态核是最小群同余,得到了这类特殊同余的交也是最小群同余的结论.3.从双循环半群上的同余关系出发,证明了双循环半群上的一类同余ρd(d ∈ N)与其逆子半群之间的相互唯一确定关系,并对这种同余做成的集合以及逆子半群做成的集合进行了刻画,证明了这种同余做成的格与自然数集在某种偏序下做成的格同构,接着对双循环半群上与Green关系有关的问题作进一步探究,得到了与之有关的结论.
[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，

本文编号：1770629