The set of all formal Laurent series is a ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.5 Let $F$ be a field and define the ring $F((x))$ of formal Laurent series with coefficients…
Prove that a given function is a valuation and find its corresponding valuation ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.27 A specific example of a discrete valuation ring is obtained when $p$ is a prime, $K…
Basic properties of discrete valuations
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.26 Let $K$ be a field. A discrete valuation on $K$ is a function $v : K^\times…