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[12] viXra:2212.0116 [pdf] submitted on 2022-12-11 02:56:23
Authors: Juan Elias Millas Vera
Comments: 24 Pages.
In this paper I am going to explain and compare some of the different tetration notations and properties for the tetration concept. Then I am going to incorporate some tables of reference for numerical tetration.
Category: Algebra
[11] viXra:2212.0103 [pdf] submitted on 2022-12-09 13:46:08
Authors: Florentin Smarandache
Comments: 11 Pages.
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 be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosophication, we split the nonempty space we work on into three regions.
Category: Algebra
[10] viXra:2212.0102 [pdf] submitted on 2022-12-09 13:46:48
Authors: Florentin Smarandache
Comments: 3 Pages.
In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.
Category: Algebra
[9] viXra:2212.0101 [pdf] submitted on 2022-12-09 13:47:36
Authors: Florentin Smarandache
Comments: 25 Pages.
In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be 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.
Category: Algebra
[8] viXra:2212.0100 [pdf] submitted on 2022-12-09 13:48:42
Authors: Mohammad Hamidi, Florentin Smarandache
Comments: 8 Pages.
This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate. While for an axiom: equal, non-equal, or indeterminate. This study investigates the Neutro-BCK-algebra and shows that Neutro-BCK-algebra are different from BCKalgebra. The notation of Neutro-BCK-algebra generates a new concept of NeutroPoset and Neutro-Hassdiagram for NeutroPosets. Finally, we consider an instance of applications of the Neutro-BCK-algebra.
Category: Algebra
[7] viXra:2212.0099 [pdf] submitted on 2022-12-09 13:49:40
Authors: Florentin Smarandache, Akbar Rezaei, Hee Sik Kim
Comments: 8 Pages.
In this paper, as an extension of CI-algebras, we discuss the new notions of Neutro-CI-algebras and Anti-CI-algebras. First, some examples are given to show that these definitions are different. We prove that any proper CI-algebra is a Neutro-BE-algebra or Anti-BE-algebra. Also, we show that any NeutroSelf-distributive and AntiCommutative CIalgebras are not BE-algebras.
Category: Algebra
[6] viXra:2212.0097 [pdf] submitted on 2022-12-09 13:51:37
Authors: Vasantha Kandasamy, Florentin Smarandache
Comments: 6 Pages.
In this paper authors for the first time define a new notion called neutrosophic lattices. We define few properties related with them. Three types of neutrosophic lattices are defined and the special properties about these new class of lattices are discussed and developed. This paper is organised into three sections. First section introduces the concept of partially ordered neutrosophic set and neutrosophic lattices. Section two introduces different types of neutrosophic lattices and the final section studies neutrosophic Boolean algebras. Conclusions and results are provided in section three.
Category: Algebra
[5] viXra:2212.0096 [pdf] submitted on 2022-12-09 13:52:19
Authors: Florentin Smarandache
Comments: 5 Pages.
Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. We now introduce for the first time the notions of neutrosophic measure and neutrosophic integral. Neutrosophic Science means development and applications of neutrosophic logic/set/measure/integral/ probability etc. and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve.
Category: Algebra
[4] viXra:2212.0086 [pdf] submitted on 2022-12-09 14:01:16
Authors: Florentin Smarandache
Comments: 5 Pages.
This paper introduces the Universal NeutroAlgebra that studies the common properties of the NeutroAlgebra structures, and the Universal AntiAlgebra that studies the common properties of the AntiAlgebraic structures.
Category: Algebra
[3] viXra:2212.0067 [pdf] submitted on 2022-12-08 02:21:41
Authors: Florentin Smarandache
Comments: 6 Pages. In Spanish
In this article, the concepts of Nth Power Set of a Set, Super-Hyper-Oper-Operation, Super-Hyper-Axiom, SuperHyper-Algebra, and their corresponding Neutrosophic Super-Hyper-Oper-Operation, Neutrosophic Super-Hyper-Axiom and Neutrosophic Super-Hyper-Algebra are reviewed. In general, in any field of knowledge, really what are found are Super-HyperStructures (or more specifically Super-Hyper-Structures (m, n)).
Category: Algebra
[2] viXra:2212.0057 [pdf] submitted on 2022-12-06 16:03:41
Authors: Florentin Smarandache
Comments: 7 Pages.
In this paper, one recalls the general definition of the SuperHyperAlgebra with its SuperHyperOperations and SuperHyperAxioms. Then one introduces for the first time the SuperHyperTopology and especially the SuperHyperFunction and Neutrosophic SuperHyperFunction. One gives a numerical example of a Neutro-SuperHyperGroup.
Category: Algebra
[1] viXra:2212.0056 [pdf] submitted on 2022-12-06 16:06:54
Authors: Florentin Smarandache
Comments: 8 Pages.
In this paper we recall our concepts of n th-Power Set of a Set, SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one actually encounters SuperHyperStructures (or more accurately (m, n)- SuperHyperStructures).
Category: Algebra
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