Left I-quotients of band of right cancellative monoids

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.

Left I-quotients of band of right cancellative monoids Keywords:

I-orders , I-quotients , right cancellative monoid , inverse hull