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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2023 • Question 4

Question

Math 6310 • Algebra Spring 2023 • Question 4

Suppose \(R\) is a commutative ring and \(I\) is an ideal. Let

\[ J=\{x\in R\mid x^n\in I\text { for some integer }n>0\}. \]

Prove directly that \(J\) is an ideal of \(R\).

Raw LaTeX

Suppose \(R\) is a commutative ring and \(I\) is an ideal. Let

\[
J=\{x\in R\mid x^n\in I\text{ for some integer }n>0\}.
\]


Prove directly that \(J\) is an ideal of \(R\).

Topic Tags

Ideals and Quotient Rings Ideals in Quadratic Integer Rings and Exterior Powers