Embed a ring of quadratic integers in a ring of matrices
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.12 Solution: We begin with a lemma. Lemma: If $D \in \mathbb{Z}$ is not a perfect square,…
Construct elements of infinite multiplicative order in some quadratic integer rings
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.24 Show that for $D \in \{ 3,5,6,7 \}$ the group of units in $\mathbb{Z}[\omega]$ is infinite…