A Property of the Weak Subalgebra Lattice for Algebras with Some Non-Equalities
Konrad Pióro · Kyungpook mathematical journal · 2010
Let A be a locally finite total algebra of finite type such that k A (a1, . . ., an) = ai for every operation k A , elements a1, . . ., an and 1 ≤ i ≤ n.We show that the weak subalgebra lattice of A uniquely determines its (strong) subalgebra lattice.More precisely, for any algebra B of the same finite type, if the weak subalgebra lattices of A and B are isomorphic, then their subalgebra lattices are also isomorphic.Moreover, B is also total and locally finite.