if \varphi : R_1 \to R_2 is a ring homomorphism, and if \mathfrak p \subset R_2 is a prime ideal, then \varphi ^{-1}(\mathfrak p) is a prime ideal of R_1,
if \varphi : R_1 \to R_2 is a ring homomorphism, and if \mathfrak p \subset R_2 is a prime ideal, then \varphi ^{-1}(\mathfrak p) is a prime ideal of R_1,
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