assignmetns.html
| Section 6.3: 11, 17, 19 |
|---|
| Section 10.1: 24, 25, 26, 29, 30 |
|---|
| Section 10.2: 2, 19, 30, 31 |
|---|
| Show that \(\mathbb{Z}[i]\) is a Euclidean domain. |
|---|
| Section 6.3: 25 |
|---|
| Section 10.1: 31, 32 |
|---|
| Section 10.2: 32, 33, 36 |
|---|
| 1. Find all units of \(\mathbb{Z}[i]\) |
|---|
| 2. Let \(R\) be a Euclidean domain with norm
\(\delta\). Show that an element \(a\) in \(R\) is a
unit if and only if \(\delta(a)=\delta(1)\). |
|---|
| 3. Find a ring that is a unique factorization
domain but not a PID, and also find a ring that is a
PID but not a Euclidean domain. |
|---|