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Title: :  THE ROLE OF NEAR-RINGS IN THE STUDY OF ALGEBRAIC STRUCTURES
PaperId: :  23886
Published in:   International Journal Of Advance Research And Innovative Ideas In Education
Publisher:   IJARIIE
e-ISSN:   2395-4396
Volume/Issue:    Volume 10 Issue 3 2024
DUI:    16.0415/IJARIIE-23886
Licence: :   IJARIIE is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Author NameAuthor Institute
E.THAMBIRAJATAMILNADU OPEN UNIVERSITY

Abstract

MATHEMATICS
Near-Rings, Algebraic Geometry, Algebraic Structures, Polynomial Identities, Commutative Algebra.
Algebraic structures are collections of solutions to systems of polynomial equations. Near-rings can be used to study these structures, as they provide a framework for analyzing the structure and properties of geometric structures in algebraic geometry. In this abstract, we will discuss some of the key concepts and results related to the use of near-rings in studying algebraic structures: a). Near-rings and their properties: A near-ring is a set equipped with two binary operations that generalize the properties of addition and multiplication in a ring. Some important properties of near-rings include being commutative, associative, and having a unit element (an identity for both operations). b). Algebraic structures: An algebraic structure is a set of points that are solutions to a system of polynomial equations. In this context, we can use near-rings to study the structure of these sets by considering the operations on the polynomial ring over a field as the near-ring operations. This allows us to analyse the behaviour of the polynomials and their zeros in the algebraic structures. c). Applications: The use of near-rings in studying algebraic structures has been applied to various areas, including commutative algebra, algebraic geometry, and algebraic combinatorics. Some specific applications include studying the structure of affine spaces, analysing the singularities of algebraic structures, and understanding the relationship between polynomial identities and algebraic geometry. In conclusion, near-rings provide a powerful tool for studying algebraic structures and their properties in algebraic geometry. By extending the concepts of rings to a more general framework, we can gain new insights into the structure and behaviour of geometric structures in this field.

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IJARIIE E.THAMBIRAJA. "THE ROLE OF NEAR-RINGS IN THE STUDY OF ALGEBRAIC STRUCTURES" International Journal Of Advance Research And Innovative Ideas In Education Volume 10 Issue 3 2024 Page 1837-1845
MLA E.THAMBIRAJA. "THE ROLE OF NEAR-RINGS IN THE STUDY OF ALGEBRAIC STRUCTURES." International Journal Of Advance Research And Innovative Ideas In Education 10.3(2024) : 1837-1845.
APA E.THAMBIRAJA. (2024). THE ROLE OF NEAR-RINGS IN THE STUDY OF ALGEBRAIC STRUCTURES. International Journal Of Advance Research And Innovative Ideas In Education, 10(3), 1837-1845.
Chicago E.THAMBIRAJA. "THE ROLE OF NEAR-RINGS IN THE STUDY OF ALGEBRAIC STRUCTURES." International Journal Of Advance Research And Innovative Ideas In Education 10, no. 3 (2024) : 1837-1845.
Oxford E.THAMBIRAJA. 'THE ROLE OF NEAR-RINGS IN THE STUDY OF ALGEBRAIC STRUCTURES', International Journal Of Advance Research And Innovative Ideas In Education, vol. 10, no. 3, 2024, p. 1837-1845. Available from IJARIIE, https://ijariie.com/AdminUploadPdf/THE_ROLE_OF_NEAR_RINGS_IN_THE_STUDY_OF_ALGEBRAIC_STRUCTURES_ijariie23886.pdf (Accessed : ).
Harvard E.THAMBIRAJA. (2024) 'THE ROLE OF NEAR-RINGS IN THE STUDY OF ALGEBRAIC STRUCTURES', International Journal Of Advance Research And Innovative Ideas In Education, 10(3), pp. 1837-1845IJARIIE [Online]. Available at: https://ijariie.com/AdminUploadPdf/THE_ROLE_OF_NEAR_RINGS_IN_THE_STUDY_OF_ALGEBRAIC_STRUCTURES_ijariie23886.pdf (Accessed : )
IEEE E.THAMBIRAJA, "THE ROLE OF NEAR-RINGS IN THE STUDY OF ALGEBRAIC STRUCTURES," International Journal Of Advance Research And Innovative Ideas In Education, vol. 10, no. 3, pp. 1837-1845, May-Jun 2024. [Online]. Available: https://ijariie.com/AdminUploadPdf/THE_ROLE_OF_NEAR_RINGS_IN_THE_STUDY_OF_ALGEBRAIC_STRUCTURES_ijariie23886.pdf [Accessed : ].
Turabian E.THAMBIRAJA. "THE ROLE OF NEAR-RINGS IN THE STUDY OF ALGEBRAIC STRUCTURES." International Journal Of Advance Research And Innovative Ideas In Education [Online]. volume 10 number 3 ().
Vancouver E.THAMBIRAJA. THE ROLE OF NEAR-RINGS IN THE STUDY OF ALGEBRAIC STRUCTURES. International Journal Of Advance Research And Innovative Ideas In Education [Internet]. 2024 [Cited : ]; 10(3) : 1837-1845. Available from: https://ijariie.com/AdminUploadPdf/THE_ROLE_OF_NEAR_RINGS_IN_THE_STUDY_OF_ALGEBRAIC_STRUCTURES_ijariie23886.pdf
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