## Characterization of zero divisors in a polynomial ring

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.2 Let $R$ be a commutative ring with $1 \neq 0$. Let $p(x) = \sum_{i=0}^n a_ix^i$ be…

## Exhibit an action of Sym(4) on a set of polynomials

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.2 Exercise 2.2.13 Let $n$ be a positive integer and let $R$ be the set of all polynomials with…

## Sym(4) acts on a set of polynomials by permuting the variables

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.2 Exercise 2.2.12 Let $R$ be the set of all polynomials with integers coefficients in the independent variables $x_1,…