NeutroAlgebra is a Generalization of Partial Algebra

Abstract

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019
research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively
AntiAlgebraic Structures).
Let <A> be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we
split the nonempty space we work on into three regions {two opposite ones corresponding to <A> and <antiA>, and
one corresponding to neutral (indeterminate) <neutA> (also denoted <neutroA>) between the opposites}, which may
or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space).
A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for
some elements, indeterminate for other elements, and false for the other elements).
A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true
for all elements).
Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of
NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation).