Semi Ideal and Semi Filter in Distributive Q lattices

Abstract

In this paper, We define concepts of prime semi ideal, prime semi filter in distributive q - lattice A and we prove A non empty subset F of A ( F≠A) is prime semi filter if and only if ( A - F) is prime semi ideal. We define concepts of semi a - ideal, semi a - filter and prove if F be semi a - filter in A then F is maximal semi a - filter if for x ∉ F there exists y ∈ F such that a = y Ë„ x , and some equivalent conditions. We define a semi - ideal Pââ€Â´ = { x ∈ A / x Ë„ a = s for all a ∈ P } and some properties. If f: A → A′ be an onto homomorphism then we prove for any semi ideal Iââ€Â´ of A , f( Iââ€Â´) is semi ideal of A′