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## Compute the powers of a given ideal in a polynomial ring

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.36 Solution: We begin with a lemma. Lemma: If $R$ is a commutative ring with 1 and…

## Some more properties of ideal arithmetic

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.35 Solution: (1) We show that $I(J+K) = IJ + IK$; the proof of the other equality…

## Some properties of ideal arithmetic

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.34 Solution: (1) We wish to prove the following: (a) $I+J$ is an ideal of $R$ and…