Reducing the axioms of hypergroups, hyperfields, hypermomules and related structures. A new axiomatic basis for hypercompositional structures

Abstract

This paper is concerned with the axiomatic basis of structures within Hypercompositional Algebra. It is proven that the axioms employed in the definition of numerous hypercompositional structures lack independence. Accordingly, novel definitions are introduced in this work which minimize the established definitions by reducing the necessary set of axioms.