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- Distributive_homomorphism abstract "A congruence θ of a join-semilattice S is monomial, if the θ-equivalence class of any element of S has a largest element. We say that θ 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 μ : 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 μ(c)≤ a ∨ b, there are elements x and y of S such that c≤ x ∨ y, μ(x)≤ a, and μ(y)≤ b.Examples:(1) For an algebra B and a reduct A of B (that is, an algebra with same underlying set as B but whose set of operations is a subset of the one of B), the canonical (∨, 0)-homomorphism from Conc A to Conc B is weakly distributive. Here, Conc A denotes the (∨, 0)-semilattice of all compact congruences of A.(2) For a convex sublattice K of a lattice L, the canonical (∨, 0)-homomorphism from Conc K to Conc L is weakly distributive.".
- Distributive_homomorphism wikiPageID "9754647".
- Distributive_homomorphism wikiPageRevisionID "525871684".
- Distributive_homomorphism hasPhotoCollection Distributive_homomorphism.
- Distributive_homomorphism subject Category:Algebra.
- Distributive_homomorphism comment "A congruence θ of a join-semilattice S is monomial, if the θ-equivalence class of any element of S has a largest element. We say that θ 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).".
- Distributive_homomorphism label "Distributive homomorphism".
- Distributive_homomorphism sameAs m.02pr57t.
- Distributive_homomorphism sameAs Q5283212.
- Distributive_homomorphism sameAs Q5283212.
- Distributive_homomorphism wasDerivedFrom Distributive_homomorphism?oldid=525871684.
- Distributive_homomorphism isPrimaryTopicOf Distributive_homomorphism.