Kasch not semilocal ring 

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

$M_n(F_q)$ 

O'Meara's infinite matrix algebra 

$T_2(F_2)$ 

Chase's leftnotright semihereditary ring 

Clark's uniserial ring 

Real numbers: $\mathbb R$ 

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

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

Šter's clean ring with nonclean corner rings 

$T_n(F)$: the upper triangular matrix ring over a field 

Varadarajan's leftnotright coHopfian ring 

$F_p(x)$ 

Field of constructible numbers 

NonArtinian simple ring 

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

Full linear ring of a countable dimensional right vector space 

$\mathbb Z[\sqrt{5}]$ 

Algebra of differential operators on the line (1st Weyl algebra) 

Complex numbers: $\mathbb C$ 

Rightnotleft nonsingular ring 

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

Algebraic integers 

Bergman's rightnotleft primitive ring 

rightnotleft coherent ring 

FaithMenal counterexample 

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

Perfect nonArtinian ring 

Rightnotleft Noetherian triangular ring 

uncountable Boolean ring 

Interval monoid ring 

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

Bergman's primitive finite uniform dimension ring 

Dedekind finite, not stably finite ring 

Local CohenMacaulay domain which isn't regular 

Countably infinite boolean ring 

Gaussian integers: $\mathbb Z[i]$ 

Rightnotleft Artinian triangular ring 

$\mathbb Z_{(p)}$ 

Bass's rightnotleft perfect ring 

ring of holomorphic functions on $\mathbb C$ 

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

Bergman's nonunitregular subring 

Bergman's unitregular ring 

$F_2[\mathbb Q_8]$ 

$\mathbb Z[x]/(x^21)$ 

$M_n(F)$: the matrix ring over an infinite field 

Simple, nonArtinian, von Neumann regular ring 

Integers: $\mathbb Z$ 

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

Cohn's nonIBN domain 

Nonsymmetric $2$primal ring 

local rightnotleft Kasch ring 

Field of algebraic numbers 

Malcev's nonembeddable domain 

Page's leftnotright FPF ring 

$T_n(F_q)$ 

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

Dieudonne's leftnotright Noetherian ring 

Finitely cogenerated, not semilocal ring. 

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

Reversible nonsymmetric ring 

Bergman's exchange ring that isn't clean 

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

nonArtinian simple domain 

$k[[x]]$ 

Semilocal not semiperfect ring 

McGovern's commutative Zorn ring that isn't clean 

leftnotright simple socle ring 

Grams' atomic domain which doesn't satisfy ACCP 

Hurwitz quaternions 

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

Local nonIkedaNakayama ring 

Osofsky's $32$ element ring 

Rational numbers: $\mathbb Q$ 

Leftnotright Noetherian domain 

Nakayama's quasiFrobenius ring that isn't Frobenius 

rightnotleft Kasch ring 

Lipschitz quaternions 

$\mathbb H$: Hamilton's quaternions 

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