Left I-quotients of band of right cancellative monoids

Document Type : Research Paper


Al-Ghrabi University


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 $q\in Q$ can be written as $q=a^{-1}b$ for some $a,b\in S$. If we insist on $a$ and $b$ being $\er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancellative monoids with certain conditions.