On the Lattice of Congruences on Inverse Semirings
Anjan Kumar Bhuniya, Anwesha Bhuniya · Discussiones Mathematicae - General Algebra and Applications · 2008
Let S be a semiring whose additive reduct (S, +) is an inverse semigroup. The relations and k, induced by tr and ker (resp.), are congruences on the lattice C(S) of all congruences on S. For 2 C(S), we have introduced four congruences min, max, min and max on S and showed that = [ min, max] and = [ min , max ]. Dieren t properties of and have been considered here. A congruence on S is a Cliord congruence if and only if max is a distributive lattice congruence and max is a skew-ring congruence on S. If ( ) is the least distributive lattice (resp. skew-ring) congruence on S then is the least Cliord congruence on S.