University of Guilan Journal of Algebra and Related Topics 2345-3931 5 1 2017 06 01 Left I-quotients of band of right cancellative monoids 11 25 2402 10.22124/jart.2017.2402 EN N. Ghroda Al-Ghrabi University Journal Article 2017 03 07 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.<br /><br /> I-orders I-quotients right cancellative monoid inverse hull https://jart.guilan.ac.ir/article_2402_6a9e9726321356602bbe3cb751ec727a.pdf