The lattice of one-sided congruences on an inverse semigroup

Abstract We build on the description of left congruences an inverse semigroup in terms kernel and trace due to Petrich Rankin. The notion for a congruence is developed. Various properties are discussed, particular that full subsemigroup both maps onto $$\cap $$ ? -homomorphisms. It shown determined by its kernel, lattice identified as subset direct product idempotents subsemigroups. demonstrate every finitely generated join minimal idempotent separating congruence. Characterisations given semigroups Noetherian, or such Rees generated.