Distributive Homomorphism
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High Quality Content by WIKIPEDIA articles!A congruence of a join-semilattice S is monomial, if the -equivalence class of any element of S has a largest element. We say that is distributive, if it is a join, in the congruence lattice Con S of S, of monomial join-congruences of S. The following definition originates in Schmidt's 1968 work and was subsequently adjusted by Wehrung. Definition (weakly distributive homomorphisms). A homomorphism : S T between join-semilattices S and T is weakly distributive, if for all a, b in S and all c in T such that (c) a b, there are elements x and y of S such that c x y, (x) a, and (y) b.…mehr

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High Quality Content by WIKIPEDIA articles!A congruence of a join-semilattice S is monomial, if the -equivalence class of any element of S has a largest element. We say that is distributive, if it is a join, in the congruence lattice Con S of S, of monomial join-congruences of S. The following definition originates in Schmidt's 1968 work and was subsequently adjusted by Wehrung. Definition (weakly distributive homomorphisms). A homomorphism : S T between join-semilattices S and T is weakly distributive, if for all a, b in S and all c in T such that (c) a b, there are elements x and y of S such that c x y, (x) a, and (y) b.