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## The ring of formal power series over an integral domain is an integral domain

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.4 Prove that if $R$ is an integral domain then the ring $R[[x]]$ of formal power series…

## The only Boolean integral domain is Z/(2)

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.16 Prove that the only boolean ring that is an integral domain is $\mathbb{Z}/(2)$. Solution: Let $B$…

## Every subring of a field which contains 1 is an integral domain

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.12 Prove that any subring of a field which contains the identity is an integral domain. Solution:…

## In an integral domain, there are at most two square roots of 1

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.11 Prove that if $R$ is an integral domain and $x^2 = 1$ for some \$x \in…