Rings

Name % Complete
Algebraic closure of $F_2$
100%
Algebraic integers
97%
Algebra of differential operators on the line (1st Weyl algebra)
68%
$^\ast \mathbb R$: the field of hyperreal numbers
99%
Bass's right-not-left perfect ring
56.0%
Berberian's incompressible Baer ring
75%
Bergman's example showing that "compressible" is not Morita invariant
43%
Bergman's exchange ring that isn't clean
70%
Bergman's non-unit-regular subring
67%
Bergman's primitive finite uniform dimension ring
64%
Bergman's right-not-left primitive ring
35%
Bergman's unit-regular ring
67%
Chase's left-not-right semihereditary ring
59%
Clark's uniserial ring
97%
Cohn's non-IBN domain
72%
Countably infinite boolean ring
80%
Cozzens' simple V-domain
89%
Custom Krull dimension valuation ring
96%
$F_2[\mathcal Q_8]$
91%
$F_2[x,y]/(x,y)^2$
88%
Faith-Menal counterexample
35%
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
87%
Grams' atomic domain which doesn't satisfy ACCP
77%
Hochster's connected, nondomain, locally-domain ring
38%
Hurwitz quaternions
69%
Interval monoid ring
98%
Kasch not semilocal ring
73%
Kolchin's simple V-domain
89%
$k[[x]]$
96%
$k[x]$
93%
$k[x^{1/2},x^{1/4},x^{1/8},...]/(x)$
69%
$k[x_1, x_2,\ldots, x_n]$
93%
$k[[x^2,x^3]]$
94%
$k[x;\sigma]/(x^2)$ (Artinian)
90%
$k[x;\sigma]/(x^2)$ (not right Artinian)
90%
$k[x,x^{-1};\sigma]$
64%
$k[x,y]/(x^2, xy)$
76%
$k[x,y]/(x^2-y^3)$
93%
$k[x,y]_{(x,y)}/(x^2-y^3)$
81%
Left-not-right Noetherian domain
67%
Left-not-right pseudo-Frobenius ring
55.0%
Left-not-right valuation domain
89%
Lipschitz quaternions
69%
Local right-not-left Kasch ring
51%
Malcev's nonembeddable domain
60%
$\mathbb C$: 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%
$\mathbb Q\langle a,b\rangle/(a^2)$
18%
$\mathbb Q$: 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%
$\mathbb R[x]/(x^2)$
99%
$\mathbb R[x,y]$ completed $I$-adically with $I=(x^2+y^2-1)$
85%
$\mathbb R[x,y]/(x^2+y^2-1)$: ring of trigonometric functions
91%
$\mathbb R[x,y,z]/(x^2,y^2, xz,yz,z^2-xy)$
98%
$\mathbb Z/(2)$
100%
$\mathbb Z[\frac{1+\sqrt{-19}}{2}]$
93%
$\mathbb Z[i]$: the Gaussian integers
93%
$\mathbb Z\langle x,y\rangle/(y^2, yx)$
62%
$\mathbb Z/(n)$, $n$ divisible by two primes and a square
94%
$\mathbb Z/(n)$, $n$ squarefree and not prime.
100%
$\mathbb Z_{(p)}$
96%
$\mathbb Z/(p^k)$, $p$ a prime, $k>1$
99%
$\mathbb Z/(p)$, $p$ 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%
$\mathbb Z+x\mathbb Q[x]$
79%
$\mathbb Z[x]/(x^2-1)$
75%
McGovern's commutative Zorn ring that isn't clean
59%
Michler & Villemayor's right-not-left V ring
64%
$M_n(F_q)$
98%
$M_n(k)$
98%
Nagata's Noetherian infinite Krull dimension ring
88%
Nakayama's quasi-Frobenius ring that isn't Frobenius
84%
Nielsen's semicommutative ring that isn't McCoy
28.0%
Non-Artinian simple ring
37%
Non-symmetric $2$-primal ring
70%
O'Meara's infinite matrix algebra
43%
Osofsky's $32$ element ring
87%
$p$-adic integers: $\mathbb Z_p$
96%
Page's left-not-right FPF ring
59%
Perfect non-Artinian ring
86%
Perfect ring that isn't semiprimary
75%
$\prod_{i=1}^\infty F_2$
80%
$\prod_{i=1}^\infty \mathbb Q[[X,Y]]$
57.0%
Puninski's triangular serial ring
35%
reduced exchange ring which is not semiregular
67%
reduced $I_0$ ring that is not exchange
65%
Reversible non-symmetric ring
66%
Right-not-left Artinian triangular ring
69%
Right-not-left coherent ring
83%
Right-not-left Kasch ring
67%
Right-not-left Noetherian triangular ring
75%
Right-not-left nonsingular ring
80%
Ring of holomorphic functions on $\mathbb C$
97%
Semicommutative $R$ such that $R[x]$ is not semicommutative
25%
Shepherdson's domain that is not stably finite
71%
Simple, non-Artinian, von Neumann regular ring
78%
Šter's clean ring with non-clean corner rings
6%
Šter's counterexample showing "clean" is not Morita invariant
20%
$T_2(F_2)$
88%
$T_n(F_q)$
88%
$T_n(k)$: the upper triangular matrix ring over a field
88%
Varadarajan's left-not-right coHopfian ring
71%
$\widehat{\mathbb Z}$: the profinite completion of the integers
49%