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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2004 • Question 5

Question

Math 6310 • Algebra Fall 2004 • Question 5

Suppose \(R\) is a commutative Noetherian ring. Let \(R[[x]]\) denote the ring of formal power series with coefficients in \(R\). Prove that \(R[[x]]\) is Noetherian.

Raw LaTeX

Suppose \(R\) is a commutative Noetherian ring. Let \(R[[x]]\) denote the ring of formal power series
with coefficients in \(R\). Prove that \(R[[x]]\) is Noetherian.

Topic Tags

Polynomial Rings and Ring Homomorphism Kernels