Commutative rings

Kasch not semilocal ring

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

Clark's uniserial ring

Real numbers: $\mathbb R$

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

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

$F_p(x)$

Field of constructible numbers

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

Complex numbers: $\mathbb C$

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

Algebraic integers

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

Perfect non-Artinian ring

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

Gaussian integers: $\mathbb Z[i]$

$\mathbb Z_{(p)}$

ring of holomorphic functions on $\mathbb C$

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

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

Integers: $\mathbb Z$

$\mathbb Z/(p^k)$, $p$ a prime, $k>1$

Field of algebraic numbers

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

Finitely cogenerated, not semilocal ring.

$\mathbb Z/(n)$, $n$ squarefree and not prime.

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

$k[[x]]$

Semilocal not semiperfect ring

McGovern's commutative Zorn ring that isn't clean

Grams' atomic domain which doesn't satisfy ACCP

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

Local non-Ikeda-Nakayama ring

Rational numbers: $\mathbb Q$

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