Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures(revisited)

Abstract

In all classical algebraic structures, the Laws of Compositionson a given set are well-defined. But this is a restrictive case, because there are many moresituations in science and in any domain of knowledgewhen a law of composition defined on a set maybe only partially-defined (or partially true) and partially-undefined(or partially false), that we call NeutroDefined, or totally undefined (totally false)that we call AntiDefined.Again, in all classical algebraic structures, the Axioms(Associativity, Commutativity, etc.)defined on a set are totally true, but it is again a restrictive case, because similarly there are numerous situations in science and in any domain of knowledgewhen an Axiom defined on a set may be only partially-true (and partially-false), that we call NeutroAxiom, or totally false that we call AntiAxiom. Therefore,we open for the first time in 2019 new fields of research called NeutroStructures andAntiStructures respectively.