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## If a nontrivial prime ideal contains no zero divisors, then the ring is an integral domain

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.10 Solution: Let $a,b \in R$ such that $ab = 0$. Since $P$ is a prime ideal…

## Not all ideals are prime

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.9 Solution: First we show that $I$ is an ideal. To That end, let $f,g \in I$.…