LATTICE OF NEAR-RING CONGRUENCES ON SEMINEARRINGS

摘要

The bijections (i) between the set of all near-ring congruences on a seminearring S and the set of all generalised strong dense reflexive right k-ideals and (ii) between the set of all zero-symmetric near-ring congruences on a seminearring S and the set of all generalised strong dense reflexive k-ideals established in Theorems 5 and 6 (Chakraborty, Mukherjee and Sardar, 2022) (cf. Note 2,6), rcspcctivcly, have been extended to lattice isomorphisms by putting some restrictions on S. A detailed study of modularity, distributivity and completeness of these lattices has also been accomplished.