On the existence of fields in Boolean algebras

A class K is said to be a field with respect to a pair of operations A, 0 if A, 0 play in K the same role which the operations +, X play in the class of rational numbers. My aim in this paper is to determine in any boolean algebra all pairs of operations expressible in terms of addition, multiplication, and negation for which the elements are a field. Postulates for fields. The conditions that make a class K a field with respect to a pair of operations A, 0 are t given by the following seven postulates :t