ON FILTERS IN BE-ALGEBRAS

抄録

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.