某些半群的半直积的同余

【作者】 彭少玉；

【导师】 张玉芬； 李师正；

【作者基本信息】 山东师范大学 ， 基础数学， 2000， 硕士

【摘要】 本文首先定义了一种新的半群—左（右）强π—逆半群，给出并证明了左（右）强π—逆半群的一个等价定义，然后着重刻划了左强π—逆半群半直积的封闭性条件，解决了左强π—逆半群半直积的最小群同余与两个构造半群的最小群同余之间的关系，并讨论了左强π—逆半群的圈积和标准圈积。然后本文解决了π—纯正半群的半直积封闭性，由此得出了右强π—逆半群半直积的封闭性条件，继而讨论了右Clifford半群和右Cliffordπ—正则半群的半直积封闭性问题。本文最后讨论了强π—逆半群的H~*—关系是r-半素同余的充分必要条件，并借助于一种关系R，利用幂等元方法给出了π—正则半群的一个最小群同余。更多还原

【Abstract】 In this paper, we first defined a new kind of semigronp, namely left(right) strongly π-inverse semigroup, introduced and characterized the necessary and sufficient conditions for a semigroup to be left(right) strongly π-inverse, and secondly characterized the necessary and sufficient conditions for S x T to he left strongly π-inverse, determined the relation of the least group congruences between sernidirect product and the two initial semigroups, then discussed the wreath product and the standard wreath product of this new kind of semigroup. After that, we characterized the necessary and sufficient conditions for S x, T to be π-orthodox, furthermore, we characterized the necessary and sufficient conditions for S Xc. T to be right strongly π-inverse. Then we discussed the semidirect product problems of right Clifford semigroup and right Clifford π-regular semigroup. In the end, we investigated the necessary and sufficient conditions for relation on a strongly π-inverse semigroup to be a r-semiprime congruence relation, then characterized the least group congruence on a π-regular semigroup by means of the idempotents means and a relation R.更多还原