Decomposable Filters of Lattices

S. Ebrahimi Atani, M. Sedghi Shanbeh Bazari

In this paper, we introduce and investigate the latticial counterpart of the filter-theoretical concepts of prime, second and irreducible. In a manner analogous to modules over a commutative ring, the main purpose of this paper is to investigate $L$-prime filters, $L$-second filters, meet-irreducible filters and special decomposable filters of lattices.