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 ∈ Q can be written as q = a^−1 b for some a, b ∈ S. If we insist on a and b being R-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