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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2017 • Question 4

Question

Math 6310 • Algebra Fall 2017 • Question 4

Let \(R=\mathbb {Z}[i]\) and \(S=\mathbb {Z}[\sqrt {-3}]\). Does there exist a ring homomorphism \(R\longrightarrow S\)? Does there exist a ring homomorphism \(S\longrightarrow R\)?

Raw LaTeX

Let \(R=\mathbb{Z}[i]\) and \(S=\mathbb{Z}[\sqrt{-3}]\). Does there exist a ring homomorphism
\(R\longrightarrow S\)? Does there exist a ring homomorphism \(S\longrightarrow R\)?

Topic Tags

Hom Functors and Module Homomorphisms Ideals in Quadratic Integer Rings and Exterior Powers Polynomial Rings and Ring Homomorphism Kernels