Abstract
In this paper we first give a procedure by which we generate a filter by
a subset in a transitive BE-algebra, and give some characterizations of Noetherian
and Artinian BE-algebras. Next we give the construction of quotient algebra X/F
of a transitive BE-algebra X via a filter F of X. Finally we discuss properties of
Noetherian (resp. Artinian) BE-algebras on homomorphisms and prove that let X
and Y be transitive BE-algebras, a mapping f : X → Y be an epimorphism. If X is
Noetherian (resp. Artinian), then so does Y . Conversely suppose that Y and Ker(f)
(as a subalgebra of X) are Noetherian (resp. Artinian), then so does X. Let X be a
transitive BE-algebra and F a filter of X. If X is Noetherian (resp. Artinian), then
so does the quotient algebra X/F.
