左同元半群的分层方法
Semigroups of left quotients - the layered approach
摘要：
半群Q的子半群S是Q中的左序，Q是S的左序半群，如果Q的每个元素都可以表示为a# b，其中a和b是S的元素，并且如果S的每个平方可消元素都位于Q的子群中。这里a#表示Q的子群中a的逆。我们说一个左序S在Q中是直的，如果在上面的定义中我们可以坚持a通过Q中的格林关系R与b相关。一个完整的刻画直左订单方面的嵌入 *-对是可用的。在本文中，我们采用了不同的方法，基于半群的偏序分解。这种分解包括半格分解和半群到主因子或主 *-因子的分解。我们确定当一个半群可以分解成直左序本身是直左序。这种技术提供了一个统一的方法来获得许多早期的结果的特点直左订单。
英文摘要：
A subsemigroup S of a semigroup Q is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be expressed as a# b where a and b are elements of S and if, in addition, every element of S that is square cancellable lies in a subgroup of Q. Here a# denotes the inverse of a in a subgroup of Q. We say that a left order S is straight in Q if in the above definition we can insist that a is related to b by Green's relation R in Q. A complete characterisation of straight left orders in terms of embeddable *-pairs is available. In this paper we adopt a different approach, based on partial order decompositions of semigroups. Such decompositions include semilattice decompositions and decompositions of a semigroup into principal factors or principal *-factors. We determine when a semigroup that can be decomposed into straight left orders is itself a straight left order. This technique gives a unified approach to obtaining many of the early results on characterisations of straight left orders.
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