Advancing Fuzzy Algebra: Polynomial Subrings, Zero Divisors, and Related Properties

Authors

  • Dinesh Kute Research Scholar
  • Dr. Arundhati Warke
  • Dr. Anil khairnar

Keywords:

Fuzzy subring, Fuzzy zero divisor, Fuzzy polynomial subring, Fuzzy McCoy subring, Fuzzy reduced subring, Fuzzy Armendariz subring

Abstract

This paper aims to expand classical ring theory into the fuzzy context, thereby strengthening the theoretical framework of fuzzy algebra. It introduces various types of fuzzy subrings, including fuzzy polynomial subrings and fuzzy matrix subrings, and explores their properties using the concept of fuzzy zero divisors. A significant contribution of this work is the development of the McCoy theorem for fuzzy polynomial subrings, leading to the definition of fuzzy McCoy subrings. Further, by building upon the notion of fuzzy zero divisors, the paper defines new classes of fuzzy subrings, such as fuzzy Armendariz subrings and fuzzy reduced subrings, and examines their fundamental properties and interconnections.

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Author Biographies

Dr. Arundhati Warke

Department of Mathematics, Symbiosis Institute of Technology (SIT), Symbiosis International (Deemed University) (SIU), Pune, Maharashtra, India

Dr. Anil khairnar

Department of Mathematics, Abasaheb Garware College, Pune, Maharashtra, India

Published

13-08-2025

How to Cite

Kute, D., Dr. Arundhati Warke, & Dr. Anil khairnar. (2025). Advancing Fuzzy Algebra: Polynomial Subrings, Zero Divisors, and Related Properties. Communications in Mathematics and Applications, 16(1). Retrieved from https://www.journals.rgnpublications.com/index.php/cma/article/view/2991

Issue

Vol. 16 No. 1 (2025)

Section

Research Article

License

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