On Finite And Infinite Neutrorings Of Type Nr

Download or read book On Finite and Infinite NeutroRings of Type-NR written by A.A.A. Agboola and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: NeutroRings in some cases exhibit different algebraic properties, and in some cases they exhibit algebraic properties similar to the classical rings. The objective of this paper is to revisit the concept of NeutroRings and study finite and infinite NeutroRings of type-NR [8,9]. In NeutroRings of type-NR [8,9], the left and right distributive axioms are taking to be either partially true or partially false for some elements; while all other classical laws and axioms are taking to be totally true for all the elements. NeutroSubrings, NeutroIdeals, NeutroQuotientRings and NeutroRingHomomorphisms of the NeutroRings of type-NR[8,9] are studied with several interesting examples and their basic properties are presented.

Download or read book International Journal of Neutrosophic Science (IJNS) Volume 11, 2020 written by Broumi Said and published by Infinite Study. This book was released on with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. Papers concern with neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributions to economics, finance, management, industries, electronics, and communications are promoted.

Download or read book Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras written by Smarandache, Florentin and published by IGI Global. This book was released on 2022-04-15 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are well-defined, but this is a restrictive case because there are situations in science where a law of composition defined on a set may be only partially defined and partially undefined, which we call NeutroDefined, or totally undefined, which we call AntiDefined. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebra introduces NeutroAlgebra, an emerging field of research. This book provides a comprehensive collection of original work related to NeutroAlgebra and covers topics such as image retrieval, mathematical morphology, and NeutroAlgebraic structure. It is an essential resource for philosophers, mathematicians, researchers, educators and students of higher education, and academicians.

Download or read book NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries (revisited) written by Florentin Smarandache and published by Infinite Study. This book was released on 2021-10-01 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry. While the Non-Euclidean Geometries resulted from the total negation of one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom or even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.) and from any type of geometry such as (Euclidean, Projective, Finite, Affine, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.) Geometry, and the NeutroGeometry results from the partial negation of one or more axioms [and no total negation of no axiom] from any geometric axiomatic system and from any type of geometry. Generally, instead of a classical geometric Axiom, one may take any classical geometric Theorem from any axiomatic system and from any type of geometry, and transform it by NeutroSophication or AntiSophication into a NeutroTheorem or AntiTheorem respectively in order to construct a NeutroGeometry or AntiGeometry. Therefore, the NeutroGeometry and AntiGeometry are respectively alternatives and generalizations of the Non-Euclidean Geometries. In the second part, we recall the evolution from Paradoxism to Neutrosophy, then to NeutroAlgebra & AntiAlgebra, afterwards to NeutroGeometry & AntiGeometry, and in general to NeutroStructure & AntiStructure that naturally arise in any field of knowledge. At the end, we present applications of many NeutroStructures in our real world.

Download or read book Neutrosophic Sets and Systems, vol. 48/2022 written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-02-01 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).

Download or read book Neutrosophic Sets and Systems. An International Journal in Information Science and Engineering, Vol. 36, 2020 written by Florentin Smarandache and published by Infinite Study. This book was released on 2020-10-01 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic Sets and Systems (NSS) is an academic journal, published quarterly online and on paper, that has been created for publications of advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics etc. and their applications in any field.

Download or read book Introduction to AntiRings written by A.A.A. Agboola and published by Infinite Study. This book was released on 2020-10-01 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this paper is to introduce the concept of AntiRings. Several examples of AntiRings are presented. Specifically, certain types of AntiRings and their substructures are studied. It is shown that nonempty subsets of an AntiRing can be AntiRings with algebraic properties different from the algebraic properties of the parent AntiRing under the same binary operations. AntiIdeals, AntiQuotientRings and AntiRingHomomorphisms are studied with several examples. It is shown that the quotient of an AntiRing factored by an AntiIdeal can exhibit algebraic properties different from the algebraic properties of the AntiRing.