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Introduction to NeutroRings

2020-10-01 Mathematics
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Release : 2020-10-01
Genre : Mathematics
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Book Synopsis Introduction to NeutroRings by : A.A.A. Agboola

Download or read book Introduction to NeutroRings written by A.A.A. Agboola . This book was released on 2020-10-01. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this paper is to introduce the concept of NeutroRings by considering three NeutroAxioms (NeutroAbelianGroup (additive), NeutroSemigroup (multiplicative) and NeutroDistributivity (multiplication over addition)). Several interesting results and examples on NeutroRings, NeutroSubgrings, NeutroIdeals, NeutroQuotientRings and NeutroRingHomomorphisms are presented. It is shown that the 1st isomorphism theorem of the classical rings holds in the class of NeutroRings.

Introduction to AntiRings

2020-10-01 Mathematics
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Release : 2020-10-01
Genre : Mathematics
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Book Synopsis Introduction to AntiRings by : A.A.A. Agboola

Download or read book Introduction to AntiRings written by A.A.A. Agboola. This book was released on 2020-10-01. 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.

Introduction to NeutroHyperGroups

2020-12-01 Mathematics
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Release : 2020-12-01
Genre : Mathematics
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Book Synopsis Introduction to NeutroHyperGroups by : M. A. Ibrahim

Download or read book Introduction to NeutroHyperGroups written by M. A. Ibrahim. This book was released on 2020-12-01. Available in PDF, EPUB and Kindle. Book excerpt: NeutroSophication and AntiSophication are processes through which NeutroAlgebraic and AntiAlgebraic structures can be generated from any classical structures. Given any classical structure with m operations (laws and axioms) we can generate NeutroStructures and AntiStructures. In this paper, we introduce for the first time the concept of NeutroHyperGroups.

NeutroAlgebra Theory Volume I

2021-06-21 Architecture
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Release : 2021-06-21
Genre : Architecture
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Book Synopsis NeutroAlgebra Theory Volume I by : Florentin Smarandache

Download or read book NeutroAlgebra Theory Volume I written by Florentin Smarandache. This book was released on 2021-06-21. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers from multiple authors. In 2019 and 2020 Smarandache [1, 2, 3, 4] 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. In classical algebraic structures, all axioms are 100%, and all operations are 100% well-defined, but in real life, in many cases these restrictions are too harsh, since in our world we have things that only partially verify some laws or some operations. Using the process of NeutroSophication of a classical algebraic structure we produce a NeutroAlgebra, while the process of AntiSophication of a classical algebraic structure produces an AntiAlgebra.

On Finite and Infinite NeutroRings of Type-NR

Mathematics
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Book Synopsis On Finite and Infinite NeutroRings of Type-NR by : A.A.A. Agboola

Download or read book On Finite and Infinite NeutroRings of Type-NR written by A.A.A. Agboola. This book was released on . 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.

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