Commutative Algebra

$\mathbb{Z}$

$\mathbb{Z}_{(p)}$, where $p$ is prime

$k[t]$, where $k$ is a field

$k[t]_{(t-1)}$, where $k$ is a field

$\mathbb{F}_p[t]_{(t^2+1)}$, where $p$ is a prime congruent to $3\pmod4$