Regular ω-semigroups
Walter Douglas Munn · Glasgow Mathematical Journal · 1968
Let S be a semigroup whose set E of idempotents is non-empty. We define a partial ordering ≧ on E by the rule that e ≧ f and only if ef = f = fe. If E = {ei: i∈ N}, where N denotes the set of all non-negative integers, and if the elements of E form the chain then S is called an ω-semigroup.