Maximal, Prime and Minimal prime filters in Residuated Lattices

In this paper, by considering the notions of maximal, prime, and minimal prime filters in residual lattices, we study their properties and some examples of residuated lattices are given. It is reminded first the notion of a filter of a residuated lattice and then we show that each proper filter is contained in a maximal filter and therefore in a prime filter. We investigate the prime filters in an MTL algebra and state and prove the fundamental theorem of the prime filters for residuated lattices. We investigate the residuated lattices in which each its filter is principal, and by using the prime filters, we inspect co-annihilators. Then the notion of a minimal prime filter in a residuated lattice is introduced and a fundamental theorem for minimal prime filters in residuated lattice is stated and proved. Finally, we introduce the divisor filters in a residuated lattice and by using them; we investigate the minimal prime filters