$\mathfrak{M}-$homomorphisms of Almost Distributive Lattices (European Journal of Pure and Applied Mathematics, 2025)
An $\mathfrak{M}-$homomorphism in an Almost Distributive Lattice(ADL) is introduced, with a sufficient condition for it to be an $\mathfrak{M}-$homomorphism. The image and inverse image of an $\mathfrak{M}-$filter under such a homomorphism are shown to be $\mathfrak{M}-$filters. Sufficient conditions for a prime filter to be an $\mathfrak{M}-$filter are established, along with an equivalence between prime $\mathfrak{M}-$filters and minimal prime filters. Finally, any two distinct prime $\mathfrak{M}-$filters in an ADL are shown to be comaximal.
Keywords: Almost Distributive Lattice(ADL), $\mathfrak{M}-$homomorphism, $\mathfrak{M}-$filter, Co-dense, Co-Kernel, $+-$ADL, Dual dense, $\sqcup-$comaximal.