• SUPERSOLVABLE, SIMPLICIAL AND EULERIAN IN THE LATTICE OF WEAK CONGRUENCES

Abstract

In this paper, we study supersolvable, simplicial and Eulerian in the lattice of weak congruences. We are going to prove that if Ln is a chain of n elements then Cw(Ln) is supersolvable. Next we prove that Cw(L) is simplicial if and only if L is a two-element chain. For any lattice L, Cw(L) is not dual simplicial. Also prove that for any lattice L, Cw(L) is not Eulerian.