A network of congruences on an inverse semigroup
Mario Petrich, Norman R. Reilly · Transactions of the American Mathematical Society · 1982
A congruence ρ \rho on an inverse semigroup S S is determined uniquely by its kernel and its trace. Denoting by ρ min {\rho ^{\min }} and ρ min {\rho _{\min }} the least congruence on S S having the same kernel and the same trace as ρ \rho , respectively, and denoting by ω \omega the universal congruence on S S , we consider the sequence ω \omega , ω min {\omega ^{\min }} , ω min {\omega _{\min }} , ( ω min ) min {({\omega ^{\min }})_{\min }} , (