Advancing Fuzzy Algebra: Polynomial Subrings, Zero Divisors, and Related Properties - Kute, Dinesh; Warke, Arundhati; Khairnar, Anil (Communications in Mathematics and Applications, 2025)
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.