Branch Mathematics and Statistics Faculty and Staff Publications
Document Type
Book
Publication Date
2021
Abstract
In general, in any field of knowledge, with respect to any structure, one has the following neutrosophic triplet . They were introduced by Smarandache in 2019 and 2020.
1) A classical Structure is a structure whose all elements are characterized by the same given Relationships and Attributes and Laws.
2) A NeutroStructure is a structure that has at least one NeutroRelation or one NeutroAttribute or one NeutroLaw, and no AntiRelation and no AntiAttribute and no AntiLaw.
3) An AntiStructure is a structure that has at least one AntiRelation or one AntiAttribute or one AntiLaw.
As a particular case, in the algebraic structures, there is a neutrosophic triplet of the form .
1) An algebraic structure who’s all operations are well-defined and all axioms are totally true is called a classical Algebraic Structure (or Algebra).
2) An algebraic structure that has at least one NeutroOperation or one NeutroAxiom (and no AntiOperation and no AntiAxiom) is called a NeutroAlgebraic Structure (or NeutroAlgebra).
3) An algebraic structure that has at least one AntiOperation or one Anti Axiom is called an AntiAlgebraic Structure (or AntiAlgebra).
Therefore, a neutrosophic triplet is formed: , where “Algebra” can be any classical algebraic structure, such as: a groupoid, semigroup, monoid, group, commutative group, ring, field, vector space, BCK-Algebra, BCI-Algebra, etc.
Publisher
The Educational Publisher (Ohio, USA)
Language (ISO)
English
Keywords
NeutroStructure, AntiStructure, NeutroAlgebra, AntiAlgebra, NeutroGeometry, AntiGeometry, NeutroAxiom, AntiAxiom
Recommended Citation
Smarandache, Florentin; Memet Şahin; Derya Bakbak; Vakkas Uluçay; and Abdullah Kargın. "NeutroAlgebra Theory, Vol. I." (2021). https://digitalrepository.unm.edu/math_fsp/565
Creative Commons License
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