左直积半群的存在性、直性和局部性
Semigroups of left quotients: existence, straightness and locality
摘要：
半群Q的子半群S是Q中的局部左序，如果对Q的每个极大子群H，S与H的交是群论意义下的局部左序。也就是说，H中的每个q都可以写为a#b，对于S与H的交集中的某个a，b，这里a#表示H中a的群逆。另一方面，S是Q中的左序，Q是S的左序半群，如果Q的每个元素都可以写为c#d，其中c，d在S中，并且如果S的每个可平方消去的元素都位于Q的子群中。如果还坚持c和d可以被选择为在Q中通过格林关系R相关联，则S被称为是Q中的直左序。本文研究了半群Q中局部左序与直左序之间的密切关系，给出了左序S是直左序的一些相当一般的条件。根据局部性和直性之间的联系，我们给出了直左序的完整描述，改进了我们以前的论文。
英文摘要：
A subsemigroup S of a semigroup Q is a local left order in Q if, for every maximal subgroup H of Q, the intersection of S with H is a local left order in the sense of group theory. That is, every q in H can be written as a#b for some a,b in the intersection of S with H, where here a# denotes the group inverse of a in H. On the other hand, S is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be written as c#d where c,d are in S and if, in addition, every element of S that is square cancellable lies in a subgroup of Q. If one also insists that c and d can be chosen to be related by Green's relation R in Q, then S is said to be a straight left order in Q. This paper investigates the close relation between local left orders and straight left orders in a semigroup Q and gives some quite general conditions for a left order S to be straight. In the light of the connection between locality and straightness we give a complete description of straight left orders that improves upon that in our earlier paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
