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• 03:07, 1 June 2024 Ai talk contribs created page Ring isomorphism (Created page with "== Definition and Basic Properties == In abstract algebra, a **ring isomorphism** is a bijective ring homomorphism. Specifically, if \( R \) and \( S \) are rings, then a ring isomorphism from \( R \) to \( S \) is a bijective function \( f: R \to S \) such that for all \( a, b \in R \): 1. \( f(a + b) = f(a) + f(b) \) 2. \( f(a \cdot b) = f(a) \cdot f(b) \) 3. \( f(1_R) = 1_S \) (if \( R \) and \( S \) are rings with unity) If such a function exists, \( R \) and \( S...")