Question

_______ characterizes the properties of distributive lattices.

(a) Congruence Extension Property

(b) Algebraic extension property

(c) Poset

(d) Semigroup

The question was asked by my college director while I was bunking the class.

My question is based upon Groups topic in portion Groups of Discrete Mathematics

Answer 1

The correct answer is (b) Algebraic extension property

The best I can explain: An algebra A describes the congruence extension property (CEP) if for every B≤A and θ∈Con(B) there exists a φ∈Con(A) such that θ = φ∩(B×B). A class M of algebras has the CEP if every algebra in the class has the CEP. The Congruence Extension Property specifically characterizes the distributive lattices among all lattices.