NeutroAlgebra of Neutrosophic Triplets using {Zn, ×}

Abstract

Smarandache in 2019 has generalized the algebraic structures to NeutroAlgebraic structures and AntiAlgebraic structures. In this paper, authors, for the first time, define the NeutroAlgebra of neutrosophic triplets group under usual+ and x, built using {Zn , x}, n a composite number, 5 < n < oo, which are not partial algebras. As idempotents in Z n alone are neutrals that contribute to neutrosophic triplets groups, we analyze them and build NeutroAlgebra of idempotents under usual + and x, which are not partial algebras. We prove in this paper the existence theorem for NeutroAlgebra of neutrosophic triplet groups. This proves the neutrals assocaited with neutrosophic triplet groups in { Zn , X} under product is a NeutroAlgebra of triplets. We also prove the non-existence theorem of NeutroAlgebra for neutrosophic triplets in case of Z n when n = 2p, 3p and 4p (for some primes p). Several open problems are proposed. Further, the NeutroAlgebras of extended neutrosophic triplet groups have been obtained.

Keywords

• neutrosophic triplets
• neutrosophic extended triplets
• neutrosophic triplet group
• neutrosophic extended triplet group
• neutroalgebra
• partial algebra
• neutroalgebra of neutrosophic triplets
• neutroalgebra of neutrosophic extended triplets
• antialgebra