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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2020 • Question 1

Question

Math 6310 • Algebra Summer 2020 • Question 1

Let \(R\) be a commutative Noetherian ring, and let \(\varphi :R\longrightarrow R\) be a surjective ring homomorphism. Is \(\varphi \) necessarily an isomorphism?

Raw LaTeX

Let \(R\) be a commutative Noetherian ring, and let \(\varphi:R\longrightarrow R\) be a
surjective ring homomorphism. Is \(\varphi\) necessarily an isomorphism?

Topic Tags

Hom Functors and Module Homomorphisms Polynomial Rings and Ring Homomorphism Kernels