Download or read book On clean neutrosophic rings written by Suryoto and published by Infinite Study. This book was released on with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: A commutative ring is said to be clean if every element of the ring can be written as a sum of a unit and an idempotent. In this paper, we generalize this argument to structure of neutrosophic. We present the structure of clean neutrosophic ring. Some elementary properties of clean neutrosophic ring are also presented.
Download or read book Refined Neutrosophic Rings I written by E.O. Adeleke and published by Infinite Study. This book was released on with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of refined neutrosophic rings is the objective of this paper. Substructures of refined neutrosophic rings and their elementary properties are presented. It is shown that every refined neutrosophic ring is a ring.
Download or read book On Some Special Elements in Neutrosophic Rings and Refined Neutrosophic Rings written by Mohammad Abobala and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Idempotent elements in a ring 𝑅 are the elements with the condition 𝒂𝟐=𝒂. This paper introduces the criterion of any element in a refined neutrosophic ring to be idempotent. Also, the concept of symmetric and supersymmetric elements in a neutrosophic ring 𝑅(𝐼), and a refined neutrosophic ring 𝑅(𝐼1,𝐼2) are defined. Also, the invertibility of these elements is discussed.
Download or read book n Refined Neutrosophic Rings written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to introduce the concept of n-refined neutrosophic ring as a generalization of refined neutrosophic ring. Also, wepresent concept of n-refined polynomial ring. We study some basic concepts related to these rings such as AH-subrings, AH-ideals, AH-factors, and AH-homomorphisms.
Download or read book n Refined Neutrosophic Rings written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to introduce the concept of n-refined neutrosophic ring as a generalization of refined neutrosophic ring. Also, wepresent concept of n-refined polynomial ring. We study some basic concepts related to these rings such as AH-subrings, AH-ideals, AH-factors, and AH-homomorphisms.
Download or read book On Clean and Nil clean Symbolic 2 Plithogenic Rings written by P. Prabakaran and published by Infinite Study. This book was released on 2023-01-01 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR.
Download or read book Neutrosophic Triplets in Neutrosophic Rings written by Vasantha Kandasamy W. B. and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition.
Download or read book Refined Neutrosophic Rings II written by E.O. Adeleke and published by Infinite Study. This book was released on with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is the continuation of the work started in the paper titled “Refined Neutrosophic Rings I”. In the present paper, we study refined neutrosophic ideals and refined neutrosophic homomorphisms along their elementary properties.
Download or read book Soft Neutrosophic Ring and Soft Neutrosophic Field written by Mumtaz Ali and published by Infinite Study. This book was released on with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields.
Download or read book Neutrosophic Units of Neutrosophic Rings and Fields written by T. Chalapathi and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the inter connection between classical structures and Neutrosophic structures is studied by few researchers. For such kind of study, researchers defined new algebraic structures whose elements are generated by elements in classical algebraic set and indeterminate of the real world problem with respect to algebraic operations on the well defined Neutrosophic elements.
Download or read book Generalization of Neutrosophic Rings and Neutrosophic Fields written by Mumtaz Ali and published by Infinite Study. This book was released on with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present the generalization of neutrosophic rings and neutrosophic fields. We also extend the neutrosophic ideal to neutrosophic biideal and neutrosophic N-ideal.
Download or read book Self Additive Inverse Elements of Neutrosophic Rings and Fields written by T.Chalapathi and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Neutrosophic theory is an abstract branch of modern mathematics that originated from classical algebra through the composition of Neutrosophic theory. Its development started few years ago, and now a days Neutrosophic analytic methods and results are important in various fields of engineering science and applied mathematics with its applications.
Download or read book A Study of Nil Ideals and Kothe s Conjecture in Neutrosophic Rings written by Mohammad Abobala and published by Infinite Study. This book was released on with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this study is to determine the necessary and sufficient condition for any AH subset to be a full ideal in a neutrosophic ring R(I) and to be a nil ideal too. Also, this work shows the equivalence between Kothe’s conjecture in classical rings and corresponding neutrosophic rings, i.e., it proves that Kothe’s conjecture is true in the neutrosophic ring R(I) if and only if it is true in the corresponding classical ring R.
Download or read book Theory on Duplicity of Finite Neutrosophic Rings written by T. Chalapathi and published by Infinite Study. This book was released on 2023-01-01 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article introduces the notion of duplex elements of the finite rings and corresponding neutrosophic rings. The authors establish duplex ring Dup(R) and neutrosophic duplex ring Dup(R)I)) by way of various illustrations. The tables of different duplicities are constructed to reveal the comparison between rings Dup(Zn), Dup(Dup(Zn)) and Dup(Dup(Dup(Zn ))) for the cyclic ring Zn . The proposed duplicity structures have several algebraic systems with dissimilar consequences. Author’s characterize finite rings with R + R is different from the duplex ring Dup(R). However, this characterization supports that R + R = Dup(R) for some well known rings, namely zero rings and finite fields.
Download or read book Generalization of Soft Neutrosophic Rings and Soft Neutrosophic Fields written by Mumtaz Ali and published by Infinite Study. This book was released on with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we extend soft neutrosophic rings and soft neutrosophic fields to soft neutrosophic birings, soft neutrosophic N-rings and soft neutrosophic bifields and soft neutrosophic N-fields.
Download or read book Neutrosophic Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2006-01-01 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on algebraic structure of group rings is one of the leading, most sought-after topics in ring theory. The new class of neutrosophic rings defined in this book form a generalization of group rings and semigroup rings.The study of the classes of neutrosophic group neutrosophic rings and S-neutrosophic semigroup neutrosophic rings which form a type of generalization of group rings will throw light on group rings and semigroup rings which are essential substructures of them. A salient feature of this group is the many suggested problems on the new classes of neutrosophic rings, solutions of which will certainly develop some of the still open problems in group rings.Further, neutrosophic matrix rings find applications in neutrosophic models like Neutrosophic Cognitive Maps (NCM), Neutrosophic Relational Maps (NRM), Neutrosophic Bidirectional Memories (NBM) and so on.
Download or read book Neutrosophic Invertible Graphs of Neutrosophic Rings written by T. Chalapathi and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: We begin by considering some properties of the self and mutual additive inverse elements of finite Neutrosophic rings. We then proceed to determine several properties of Neutrosophic invertible graphs and we obtain an interrelation between classical rings, Neutrosophic rings and their Neutrosophic invertible graphs.
