Biordered sets are biordered subsets of idempotents of semigroups
David Easdown · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1984
Abstract A new arrow notation is used to describe biordered sets. Biordered sets are characterized as biordered subsets of the partial algebras formed by the idempotents of semigroups. Thus it can be shown that in the free semigroup on a biordered set factored out by the equations of the biordered set there is no collapse of idempotents and no new arrows.