A class of archimedean lattice ordered algebras

Abstract.

This paper introduces a ‘new’ class of lattice ordered algebras. A lattice ordered algebra A will be called a pseudo f-algebra if xy = 0 for all x, y in A such that x ⋀ y is a nilpotent element in A. Dierent aspects of archimedean pseudo f-algebras are considered in detail. Mainly their integral representations on spaces of continuous functions, as well as their connection with almost f-algebras and f-algebras. Various characterizations of order bounded multiplicators on pseudo f-algebras are given, where by a multiplicator on a pseudo f-algebra A we mean an operator T on A such that xT(y) = yT(x) for all x, y in A. In this regard, it will be focused on the relationship between multiplicators and orthomorphisms on pseudo f-algebras.