A Certain Structure of Bipolar Fuzzy Subrings

The role of symmetry in ring theory is universally recognized. most directly definable universal relation a symmetric set isomorphism. This article develops certain structure bipolar fuzzy subrings, including quotient ring, homomorphism, and We define (?,?)-cut investigate the algebraic attributions this phenomenon. also support prove various important properties relating to concept. Additionally, we homomorphism by using notion natural homomorphism. establish between subring ring. constituted significant relationship two subrings rings under given surjective present construction an induced isomorphism related subrings. Moreover, discuss three fundamental theorems