A NOTE ON NORMAL SUBALGEBRAS IN B-ALGEBRAS
Andrzej Walendziak · Scientiae mathematicae Japonicae · 2005
The concept of normal subalgebras in B- algebras is due to J. Neggers and H. S. Kim. We give an equivalent definition and show that the center Z(A )o f a B-algebra A is a normal subalgebra of A. Moreover, we prove that the notion of a normal subalgebra is equivalent to the normal subgroup of the derived group. Hence the lattices of normal subalgebras (and also the congruence lattices) of B-algebras are modular. 1 Preliminaries B-algebras have been introduced by J. Neggers and H. S. Kim in (4). They defined a B-algebra as an algebra (A; ∗,0) of type (2,0) (i.e., a nonempty set A with a binary operation ∗ and a constant 0) satisfying the following axioms: