A Algebra definitions

If a lattice L is distributive, then L is also modular . By assuming x y, we have x y = y . Hence, from the distributive property we get: x (y z) ( x y) (x z) y ( x z) 14 Definition A.7. Congruence Lattice Reflexivity: For every element a in A, a is related to itself, denoted as a a; Symmetry: For any elements a and b in A, if a b, then b a; Transitivity: For any elements a, b, and c in A, if a b and b c, then a c . An algebra with no other congruences is called simple . A type F is defined as a set of operation symbols along with their respective arities.