
 NeutroAlgebra
From Paradoxism to Neutrosophy Paradoxism is an international movement in science and culture, founded by
Florentin Smarandache in 1980s, based on excessive use of antitheses, oxymoron,
contradictions, and paradoxes. During three decades (19802020) hundreds of
authors from tens of countries around the globe contributed papers to 15
international paradoxist anthologies. From Classical Algebraic Structures to NeutroAlgebraic Structures and AntiAlgebraic Structures In 2019 and 2020 Smarandache [1, 2, 3] generalized the classical Algebraic Structures to NeutroAlgebraic Structures (or NeutroAlgebras) {whose operations and axioms are partially true, partially indeterminate, and partially false} as extensions of Partial Algebra, and to AntiAlgebraic Structures (or AntiAlgebras) {whose operations and axioms are totally false}. The NeutroAlgebras & AntiAlgebras are a new field of research, which is inspired from our real world.
Operation, NeutroOperation, AntiOperation When we define an operation on a given set, it does not
automatically mean that the operation is welldefined. There are three
possibilities: Axiom, NeutroAxiom, AntiAxiom Similarly for an axiom, defined on a given set, endowed with
some operation(s). When we define an axiom on a given set, it does not
automatically mean that the axiom is true for all set’s elements. We have three
possibilities again:
Algebra, NeutroAlgebra, AntiAlgebra 1) An algebraic structure who’s all
operations are welldefined and all axioms are totally true is called Classical
Algebraic Structure (or Algebra).
In general, Smarandache extended any classical Structure, in no
matter what field of knowledge, to NeutroStructure and AntiStructure. Similarly, we get the NeutroStructure and AntiStructure.
References
1. Florentin Smarandache: NeutroAlgebra is a Generalization
of Partial Algebra. International Journal of Neutrosophic Science (IJNS), Volume
2, 2020, pp. 817. DOI:
http://doi.org/10.5281/zenodo.3989285 2. F. Smarandache, Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures, in Advances of Standard and Nonstandard Neutrosophic Theories, Pons Publishing House Brussels, Belgium, Chapter 6, pages 240265, 2019; http://fs.unm.edu/AdvancesOfStandardAndNonstandard.pdf 3. Florentin Smarandache: Introduction to NeutroAlgebraic
Structures and AntiAlgebraic Structures (revisited). Neutrosophic Sets and
Systems, vol. 31, pp. 116, 2020. DOI: 10.5281/zenodo.3638232 4. Florentin Smarandache, Generalizations and Alternatives of
Classical Algebraic Structures to NeutroAlgebraic Structures and AntiAlgebraic
Structures, Journal of Fuzzy Extension and Applications (JFEA), J. Fuzzy. Ext.
Appl. Vol. 1, No. 2 (2020) 85–87, DOI: 10.22105/jfea.2020.248816.1008
6. Agboola, A.A.A: Introduction to NeutroGroups.
International Journal of Neutrosophic Science (IJNS), Volume 6, 2020, pp. 4147.
DOI:
http://doi.org/10.5281/zenodo.3989823
7. Agboola A.A.A: Introduction to NeutroRings. International
Journal of Neutrosophic Science (IJNS), Volume 7, 2020, pp. 6273. DOI:
http://doi.org/10.5281/zenodo.3991389 8. Akbar Rezaei, Florentin Smarandache: On NeutroBEalgebras
and AntiBEalgebras. International Journal of Neutrosophic Science (IJNS),
Volume 4, 2020, pp. 815. DOI:
http://doi.org/10.5281/zenodo.3989550 9. Mohammad Hamidi, Florentin Smarandache: NeutroBCKAlgebra.
International Journal of Neutrosophic Science (IJNS), Volume 8, 2020, pp.
110117. DOI:
http://doi.org/10.5281/zenodo.3991437 10. Florentin Smarandache, Akbar Rezaei, Hee Sik Kim: A New
Trend to Extensions of CIalgebras. International Journal of Neutrosophic
Science (IJNS) Vol. 5, No. 1 , pp. 815, 2020; DOI: 10.5281/zenodo.3788124 11. Florentin Smarandache: Extension of HyperGraph to nSuperHyperGraph
and to Plithogenic nSuperHyperGraph, and Extension of HyperAlgebra to nary
(Classical/Neutro/Anti)HyperAlgebra. Neutrosophic Sets and Systems, Vol. 33,
pp. 290296, 2020. DOI: 10.5281/zenodo.3783103


