Equivalent Conditions of Normal Autometrized L-algebra

Abstract

In this paper, we discuss the properties of some elements in autometrized algebra. We also introduce some properties of normal autometrized algebra. Furthermore, we obtain normal autometrized l-algebras among the normal autometrized semialgebras satisfying several conditions and discussing some of its properties. We also prove that a normal autometrized semialgebra satisfying certain conditions is a lattice and distributive. Finally, we establish an equivalent condition between normal autometrized l-algebra and representable autometrized algebra with some conditions. We also prove that in a normal autometrized l-algebra satisfying some conditions, there exists a subset which is a convex normal subalgebra.