University of GuilanJournal of Algebra and Related Topics2345-39315120170601Left I-quotients of band of right cancellative monoids1125240210.22124/jart.2017.2402ENN. GhrodaAl-Ghrabi UniversityJournal Article20170307Let $Q$ 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 $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. 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.<br /><br />https://jart.guilan.ac.ir/article_2402_6a9e9726321356602bbe3cb751ec727a.pdf