Commutative rings

$\mathbb Z[\frac{1+\sqrt{-19}}{2}]$

Kasch not semilocal ring

$\mathbb Z[x]/(x^2-1)$

$\mathbb Z/(n)$, $n$ prime

Integers: $\mathbb Z$

$\mathbb Z/(n)$, $n$ a prime power

Field of algebraic numbers

Clark's uniserial ring

Real numbers: $\mathbb R$

$F[x^{1/2},x^{1/4},x^{1/8},...]/(x)$

$\Bbb Q[X,Y]_{(X,Y)}$

$\mathbb R[x]/(x^2)$

Finitely cogenerated, not semilocal ring.

$\mathbb Z/(n)$, $n$ squarefree

$k[[x^2,x^3]]$

$k[[x]]$

$F_p(x)$

Semilocal not semiperfect ring

Field of constructible numbers

$\mathbb Z+x\mathbb Q[x]$

Complex numbers: $\mathbb C$

Grams' atomic domain which doesn't satisfy ACCP

$\mathbb R[x,y,z]/(x^2,y^2, xz,yz,z^2-xy)$

Algebraic integers

Integer polynomial ring: $\mathbb Z[x]$

$\mathbb Z/(n)$, $n$ divisible by two primes and a square

Perfect nonArtinian ring

Rational numbers: $\mathbb Q$

uncountable Boolean ring

Interval monoid ring

$F_2[x,y]/(x,y)^2$

Local Cohen-Macaulay domain which isn't regular

Countably infinite boolean ring

Polynomial ring over a field: $F[x]$

ring of holomorphic functions on $\mathbb C$