### Semigroups of inverse quotients

Algebra Seminar

11th May 2022, 2:30 pm – 3:30 pm

Fry Building, Room 2.04

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 in Q can be written as a^{−1}b, where a, b ∈ S and a^{−1} is the inverse of a in the sense of inverse semigroup theory. If we insist on being able to take a and b to be R-related in Q, we say that S is straight in Q. We give a set of necessary and sufficient conditions for a semigroup to be a straight left I-order.

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