Introduction to Algebraic Geometry

  title={Introduction to Algebraic Geometry},
  author={Steven Dale Cutkosky},
  journal={Graduate Studies in Mathematics},
  • S. D. Cutkosky
  • Published 31 May 2018
  • Mathematics
  • Graduate Studies in Mathematics
Recall that a map Φ : U → V of sets is a 1-1 correspondence (a bijection) if and only if Φ has an inverse map; that is, a map Ψ : V → U such that Ψ ◦Φ = idU and Φ ◦Ψ = idV . Lemma 1.3. Let π : R→ S be a surjective ring homomorphism, with kernel K. 1. Suppose that I is an ideal in S. Then π−1(I) is an ideal in R containing K. 2. Suppose that J is an ideal in R such that J contains K. Then π(J) is an ideal in S. 3. The map I 7→ π−1(I) is a 1-1 correspondence between the set of ideals in R and the… 
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    Proceedings of the National Academy of Sciences of the United States of America
  • 1959
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