# Commutative rings

Name % Complete
$^\ast \mathbb R$: the field of hyperreal numbers
100.0%
$C([0,1])$, the ring of continuous real-valued functions on the unit interval
77.0%
$F_2[x,y]/(x,y)^2$
99.0%
$F_p(x)$
99.0%
$k[[x]]$
99.0%
$k[x]$
100.0%
$k[x^{1/2},x^{1/4},x^{1/8},...]/(x)$
72.0%
$k[x_1, x_2,\ldots, x_n]$
93.0%
$k[[x^2,x^3]]$
94.0%
$k[x,y]/(x^2, xy)$
77.0%
$k[x,y]/(x^2-y^3)$
91.0%
$k[x,y]_{(x,y)}/(x^2-y^3)$
85.0%
$k[x,y,z]/(xz,yz)$
90.0%
$\mathbb C$: the field of complex numbers
100.0%
$\mathbb F_2[x_1, x_2, x_3\ldots ]/(\{x_i^3\mid i\in \mathbb N\}\cup\{x_ix_j|i\neq j\}\cup\{x_i^2-m\mid i\in \mathbb N\})$
94.0%
$\mathbb Q$: the field of rational numbers
100.0%
$\mathbb Q[\mathbb Q]$
72.0%
$\mathbb Q(x)$: rational functions over the rational numbers
100.0%
$\mathbb Q[X,Y]_{(X,Y)}$
98.0%
$\mathbb R$: the field of real numbers
100.0%
$\mathbb R[x_1, x_2,x_3,\ldots]$
88.0%
$\mathbb R[x]/(x^2)$
99.0%
$\mathbb R[x,y]$ completed $I$-adically with $I=(x^2+y^2-1)$
81.0%
$\mathbb R[x,y]/(x^2+y^2-1)$: ring of trigonometric functions
98.0%
$\mathbb R[x,y,z]/(x^2,y^2, xz,yz,z^2-xy)$
97.0%
$\mathbb Z$: the ring of integers
100.0%
$\mathbb Z/(2)$
100.0%
$\mathbb Z[\frac{1+\sqrt{-19}}{2}]$
99.0%
$\mathbb Z[i]$: the Gaussian integers
99.0%
$\mathbb Z/(n)$, $n$ divisible by two primes and a square
97.0%
$\mathbb Z/(n)$, $n$ squarefree and not prime.
97.0%
$\mathbb Z_{(p)}$
98.0%
$\mathbb Z/(p)$, $p$ an odd prime
100.0%
$\mathbb Z/(p^k)$, $p$ a prime, $k>1$
99.0%
$\mathbb Z_S$, where $S=((2)\cup(3))^c$
99.0%
$\mathbb Z[\sqrt{-5}]$
98.0%
$\mathbb Z[x]$
97.0%
$\mathbb Z+x\mathbb Q[x]$
88.0%
$\mathbb Z[x]/(x^2-1)$
79.0%
$p$-adic integers: $\mathbb Z_p$
99.0%
$\prod_{i=1}^\infty F_2$
98.0%
$\prod_{i=1}^\infty \mathbb Q[[X,Y]]$
68.0%
$\widehat{\mathbb Z}$: the profinite completion of the integers
65.0%
Akizuki's counterexample
72.0%
Algebraic closure of $F_2$
100.0%
Algebraic integers
95.0%
Clark's uniserial ring
94.0%
Cohn's Schreier domain that isn't GCD
77.0%
Countably infinite boolean ring
91.0%
Custom Krull dimension valuation ring
95.0%
field of $p$-adic numbers
99.0%
Field of algebraic numbers
100.0%
Field of constructible numbers
100.0%
Finitely cogenerated, not semilocal ring.
84.0%
Grams' atomic domain which doesn't satisfy ACCP
75.0%
Henselization of $\Bbb Z_{(p)}$
69.0%
Hochster's connected, nondomain, locally-domain ring
54.0%
Interval monoid ring
96.0%
Kasch not semilocal ring
78.0%
McGovern's commutative Zorn ring that isn't clean
69.0%
Mori but not Krull domain
70.0%
Nagata's Noetherian infinite Krull dimension ring
87.0%
Nagata's normal ring that is not analytically normal
61.0%
Noetherian domain that is not N-1
78.0%
Noetherian ring that is not Grothendieck and not Nagata
93.0%
Perfect non-Artinian ring
92.0%
Perfect ring that isn't semiprimary
81.0%
Pseudo-Frobenius, not quasi-Frobenius ring
85.0%
reduced $I_0$ ring that is not exchange
69.0%
reduced exchange ring which is not semiregular
70.0%
Ring of holomorphic functions on $\mathbb C$
94.0%
Samuel's UFD having a non-UFD power series ring
88.0%