Rings

Name % Complete
Algebraic closure of $F_2$
100%
Algebraic integers
97%
Algebra of differential operators on the line (1st Weyl algebra)
64%
$^\ast \mathbb R$: the field of hyperreal numbers
97%
Bass's right-not-left perfect ring
57.0%
Berberian's incompressible Baer ring
76%
Bergman's example showing that "compressible" is not Morita invariant
40%
Bergman's exchange ring that isn't clean
71%
Bergman's non-unit-regular subring
66%
Bergman's primitive finite uniform dimension ring
64%
Bergman's right-not-left primitive ring
34%
Bergman's unit-regular ring
65%
Chase's left-not-right semihereditary ring
59%
Clark's uniserial ring
97%
Cohn's non-IBN domain
68%
Countably infinite boolean ring
79%
Custom Krull dimension valuation ring
97%
Dedekind finite, not stably finite ring
68%
$F_2[\mathcal Q_8]$
92%
$F_2[x,y]/(x,y)^2$
89%
Faith-Menal counterexample
34%
Field of algebraic numbers
99%
Field of constructible numbers
99%
field of $p$-adic numbers
99%
Finitely cogenerated, not semilocal ring.
85%
$F_p(x)$
99%
Full linear ring of a countable dimensional right vector space
89%
Grams' atomic domain which doesn't satisfy ACCP
76%
Hochster's connected, nondomain, locally-domain ring
36%
Hurwitz quaternions
69%
Interval monoid ring
99%
Kasch not semilocal ring
73%
$k[[x]]$
97%
$k[x]$
92%
$k[x^{1/2},x^{1/4},x^{1/8},...]/(x)$
68%
$k[x_1, x_2,\ldots, x_n]$
92%
$k[[x^2,x^3]]$
94%
$k[x,y]/(x^2, xy)$
73%
$k[x,y]/(x^2-y^3)$
92%
$k[x,y]_{(x,y)}/(x^2-y^3)$
82%
Left-not-right Noetherian domain
66%
Left-not-right simple socle ring
91%
Lipschitz quaternions
68%
Local right-not-left Kasch ring
51%
Malcev's nonembeddable domain
56.0%
$\mathbb C$: the field of complex numbers
99%
$\mathbb F_2[x_1, x_2, x_3\ldots ]/(\{x_i^3\mid i\in \mathbb N\}\cup\{x_ix_j|i\neq j\}\cup\{x_i^2-m\mid i\in \mathbb N\})$
85%
$\mathbb H$: Hamilton's quaternions
100%
$\mathbb Q$: the field of rational numbers
99%
$\mathbb Q(x)$: rational functions over the rational numbers
100%
$\mathbb Q[X,Y]_{(X,Y)}$
94%
$\mathbb R$: the field of real numbers
99%
$\mathbb R[x_1, x_2,x_3,\ldots]$
86%
$\mathbb R[x]/(x^2)$
100%
$\mathbb R[x,y]$ completed $I$-adically with $I=(x^2+y^2-1)$
79%
$\mathbb R[x,y]/(x^2+y^2-1)$: ring of trigonometric functions
91%
$\mathbb R[x,y,z]/(x^2,y^2, xz,yz,z^2-xy)$
99%
$\mathbb Z/(2)$
100%
$\mathbb Z[\frac{1+\sqrt{-19}}{2}]$
92%
$\mathbb Z[i]$: the Gaussian integers
92%
$\mathbb Z\langle x,y\rangle/(y^2, yx)$
62%
$\mathbb Z/(n)$, $n$ divisible by two primes and a square
95%
$\mathbb Z/(n)$, $n$ squarefree and not prime.
100%
$\mathbb Z_{(p)}$
97%
$\mathbb Z/(p^k)$, $p$ a prime, $k>1$
100%
$\mathbb Z/(p)$, $p$ an odd prime
100%
$\mathbb Z[\sqrt{-5}]$
91%
$\mathbb Z_S$, where $S=((2)\cup(3))^c$
98%
$\mathbb Z$: the ring of integers
99%
$\mathbb Z[x]$
93%
$\mathbb Z+x\mathbb Q[x]$
80%
$\mathbb Z[x]/(x^2-1)$
74%
McGovern's commutative Zorn ring that isn't clean
59%
Michler & Villemayor's right-not-left V ring
64%
$M_n(F_q)$
100%
$M_n(k)$
100%
Nagata's Noetherian infinite Krull dimension ring
87%
Nakayama's quasi-Frobenius ring that isn't Frobenius
85%
Non-Artinian simple domain
63%
Non-Artinian simple ring
37%
Non-symmetric $2$-primal ring
71%
O'Meara's infinite matrix algebra
43%
Osofsky's $32$ element ring
89%
$p$-adic integers: $\mathbb Z_p$
97%
Page's left-not-right FPF ring
60%
Perfect non-Artinian ring
86%
Perfect ring that isn't semiprimary
75%
$\prod_{i=1}^\infty F_2$
79%
$\prod_{i=1}^\infty \mathbb Q[[X,Y]]$
55.0%
Puninski's triangular serial ring
34%
reduced exchange ring which is not semiregular
66%
reduced $I_0$ ring that is not exchange
64%
Reversible non-symmetric ring
66%
Right-not-left Artinian triangular ring
70%
Right-not-left coherent ring
84%
Right-not-left Kasch ring
68%
Right-not-left Noetherian triangular ring
76%
Right-not-left nonsingular ring
82%
Ring of holomorphic functions on $\mathbb C$
97%
Simple, non-Artinian, von Neumann regular ring
76%
Šter's clean ring with non-clean corner rings
6%
Šter's counterexample showing "clean" is not Morita invariant
20%
$T_2(F_2)$
89%
$T_n(F_q)$
89%
$T_n(k)$: the upper triangular matrix ring over a field
89%
Varadarajan's left-not-right coHopfian ring
72%
$\widehat{\mathbb Z}$: the profinite completion of the integers
48%