论文标题
直左代理的半群
Semigroups of straight left inverse quotients
论文作者
论文摘要
令$ Q $为反向半群。 A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element in $Q$ can be written as $a^{-1}b$, where $a, b \in S$ and $a^{-1}$ is the inverse of $a$ in the sense of inverse semigroup theory.如果我们坚持认为能够将$ a $ a和$ b $作为$ \ mathcal {r} $ - 与$ q $相关，我们说$ s $在$ q $中是直的，$ q $是$ s $ $ s $的直i- Q $。我们给出了一组必要和足够的条件，使半群成为直流的i-rorder。这些条件是根据两种二进制关系的，与$ \ Mathcal {r} $和$ \ Mathcal {l} $的潜在限制相对应，以及相关的部分顺序。我们的方法依赖于反向半群的$ \ Mathcal {l} $的满足结构。我们证明，每个有限的左I级订单都是笔直的，并给出一个左I订单的示例，该订单不是笔直的。
Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element in $Q$ can be written as $a^{-1}b$, where $a, b \in S$ and $a^{-1}$ is the inverse of $a$ in the sense of inverse semigroup theory. If we insist on being able to take $a$ and $b$ to be $\mathcal{R}$-related in $Q$ we say that $S$ is straight in $Q$ and $Q$ is a semigroup of straight left I-quotients of $S$. We give a set of necessary and sufficient conditions for a semigroup to be a straight left I-order. The conditions are in terms of two binary relations, corresponding to the potential restrictions of $\mathcal{R}$ and $\mathcal{L}$ from an oversemigroup, and an associated partial order. Our approach relies on the meet structure of the $\mathcal{L}$ of inverse semigroups. We prove that every finite left I-order is straight and give an example of a left I-order which is not straight.
