Semimedial Near Rings

Dhivya C  lowast; Radha D

doi:10.17485/IJST/v17i24.1403

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i24.1403

Year: 2024, Volume: 17, Issue: 24, Pages: 2478-2481

Original Article

Semimedial Near Rings

Dhivya C^1∗, Radha D²

¹Research Scholar (Reg. No: 21112012092011), PG & Research Department of Mathematics, A.P.C. Mahalaxmi College for Women, Thoothukudi, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627012, Tamil Nadu, India
²Assistant Professor, PG & Research Department of Mathematics, A.P.C. Mahalaxmi College for Women, Thoothukudi, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627012, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:26 April 2024, Accepted Date:20 May 2024, Published Date:10 June 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: To define the term ‘semimediality’ in the near ring and to demonstrate its presence with an example and to employ several attributes in near rings to analyse its features. Methods: Semimedial near rings are examined in terms of their characteristics using commutativity, distributivity and regular property. The distinction is observed using the concept of homomorphism. Findings: Every near ring which is weak commutative is proved to be semimedial and the converse exists with some additional axioms. The semimedial near ring’s anti-homomorphic image is also observed. Additionally, the correlation between the semimedial near ring and the reduced property is identified. Novelty: This study provides a novel method to medial near ring, which is the semimedial near ring.

Keywords: Identity, Left Self Distributive, Nilpotent, Regular, Weak Commutative

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Copyright

© 2024 Dhivya C & Radha D. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)