Rings

Name % Complete
$C([0,1])$, the ring of continuous real-valued functions on the unit interval
89%
$C\ell_{2,1}(\mathbb R)$: the geometric algebra of Minkowski 3-space
97%
$C^\infty_0(\mathbb R)$: the ring of germs of smooth functions on $\mathbb R$ at $0$
70%
$F_2[S_4]$
91%
$F_2[\mathcal Q_8]$
100%
$F_2[x,y]/(x,y)^2$
99%
$F_p(x)$
100%
$M_n(F_q)$
100%
$M_n(k)$
100%
$T_2(F_2)$
99%
$T_n(F_q)$
93%
$T_n(k)$: the upper triangular matrix ring over a field
94%
$\mathbb A_\mathbb Q$: the ring of adeles of $\mathbb Q$
80%
$\mathbb C$: the field of complex numbers
100%
$\mathbb H$: Hamilton's quaternions
100%
$\mathbb Q$: the field of rational numbers
100%
$\mathbb Q(x)$: rational functions over the rational numbers
100%
$\mathbb Q[X,Y]_{(X,Y)}$
100%
$\mathbb Q[[x^2,x^3]]$
100%
$\mathbb Q[\mathbb Q]$
96%
$\mathbb Q[x]$
99%
$\mathbb Q\langle a,b\rangle/(a^2)$
55.0%
$\mathbb Q\langle x, y\rangle$
64%
$\mathbb Q\langle x,y \rangle/(xy-1)$: the Toeplitz-Jacobson algebra
63%
$\mathbb R$: the field of real numbers
100%
$\mathbb R[[x]]$
100%
$\mathbb R[x,y,z]/(x^2,y^2, xz,yz,z^2-xy)$
98%
$\mathbb R[x,y]$ completed $I$-adically with $I=(x^2+y^2-1)$
91%
$\mathbb R[x,y]/(x^2+y^2-1)$: ring of trigonometric functions
97%
$\mathbb R[x]/(x^2)$
100%
$\mathbb R[x_1, x_2,x_3,\ldots]$
90%
$\mathbb Z$: the ring of integers
99%
$\mathbb Z+x\mathbb Q[x]$
91%
$\mathbb Z/(2)$
100%
$\mathbb Z/(n)$, $n$ divisible by two primes and a square
100%
$\mathbb Z/(n)$, $n$ squarefree and not prime.
100%
$\mathbb Z/(p)$, $p$ an odd prime
100%
$\mathbb Z/(p^k)$, $p$ a prime, $k>1$
100%
$\mathbb Z[X]/(X^2,4X, 8)$
97%
$\mathbb Z[X]/(X^2,8)$
100%
$\mathbb Z[\frac{1+\sqrt{-19}}{2}]$
98%
$\mathbb Z[\sqrt{-5}]$
97%
$\mathbb Z[i]$: the Gaussian integers
98%
$\mathbb Z[x]$
96%
$\mathbb Z[x]/(x^2-1)$
83%
$\mathbb Z[x_0, x_1,x_2,\ldots]$
70%
$\mathbb Z\langle x,y\rangle/(y^2, yx)$
74%
$\mathbb Z\langle x_0, x_1,x_2,\ldots\rangle$
65%
$\mathbb Z_S$, where $S=((2)\cup(3))^c$
100%
$\mathbb Z_{(p)}$
100%
$\prod_{i=1}^\infty F_2$
100%
$\prod_{i=1}^\infty \mathbb Q[[X,Y]]$
75%
$\widehat{\mathbb Z}$: the profinite completion of the integers
74%
$^\ast \mathbb R$: the field of hyperreal numbers
100%
$k[[x,y]]/(x^2,xy)$
84%
$k[x,x^{-1};\sigma]$
80%
$k[x,y,z]/(xz,yz)$
94%
$k[x,y]/(x^2, xy)$
90%
$k[x,y]/(x^2-y^3)$
96%
$k[x,y]_{(x,y)}/(x^2-y^3)$
98%
$k[x;\sigma]/(x^2)$ (Artinian)
96%
$k[x;\sigma]/(x^2)$ (not right Artinian)
95%
$k[x^{1/2},x^{1/4},x^{1/8},...]/(x)$
69%
$k[x_1, x_2,\ldots, x_n]$
96%
$p$-adic integers: $\mathbb Z_p$
100%
10-adic numbers
89%
2-dimensional uniserial domain
87%
Akizuki's counterexample
84%
Algebra of differential operators on the line (1st Weyl algebra)
83%
Algebraic closure of $F_2$
100%
Algebraic integers
98%
Basic ring of Nakayama's QF ring
55.0%
Bass's right-not-left perfect ring
77%
Berberian's incompressible Baer ring
81%
Bergman's example showing that "compressible" is not Morita invariant
58.0%
Bergman's exchange ring that isn't clean
78%
Bergman's non-unit-regular subring
65%
Bergman's primitive finite uniform dimension ring
62%
Bergman's right-not-left primitive ring
37%
Bergman's ring with IBN
1%
Bergman's ring without IBN
32%
Bergman's unit-regular ring
66%
Camillo and Nielsen's McCoy ring
4%
Chase's left-not-right semihereditary ring
73%
Clark's uniserial ring
95%
Cohn's Schreier domain that isn't GCD
81%
Cohn's non-IBN domain
77%
Cohn's right-not-left free ideal ring
67%
Countably infinite boolean ring
92%
Cozzens simple, left principal, right non-Noetherian domain
82%
Cozzens' simple V-domain
91%
Custom Krull dimension valuation ring
99%
DVR that is not N-2
98%
Division algebra with no anti-automorphism
99%
Eventually constant sequences in $\mathbb Z$
44%
Facchini's torch ring
66%
Faith-Menal counterexample
41%
Field of algebraic numbers
100%
Field of constructible numbers
100%
Finitely cogenerated, not semilocal ring.
90%
Full linear ring of a countable dimensional right vector space
89%
Goodearl's simple self-injective operator algebra
87%
Goodearl's simple self-injective von Neumann regular ring
87%
Grams' atomic domain which doesn't satisfy ACCP
79%
Grassmann algebra $\bigwedge (V)$, $\dim(V)=\aleph_0$
70%
Henselization of $\Bbb Z_{(p)}$
99%
Hochster's connected, nondomain, locally-domain ring
85%
Hurwitz quaternions
70%
Interval monoid ring
99%
Kaplansky's right-not-left hereditary ring
63%
Kasch not semilocal ring
80%
Kerr's Goldie ring with non-Goldie matrix ring
44%
Kolchin's simple V-domain
91%
Leavitt path algebra of an infinite bouquet of circles
33%
Left-not-right Noetherian domain
73%
Left-not-right pseudo-Frobenius ring
67%
Left-not-right uniserial domain
93%
Lipschitz quaternions
70%
Local right-not-left Kasch ring
73%
Malcev's nonembeddable domain
83%
McGovern's commutative Zorn ring that isn't clean
67%
Michler & Villamayor's right-not-left V ring
71%
Mori but not Krull domain
78%
Nagata ring that not quasi-excellent
97%
Nagata's Noetherian infinite Krull dimension ring
91%
Nagata's normal ring that is not analytically normal
70%
Nakayama's quasi-Frobenius ring that isn't Frobenius
90%
Nielsen's right UGP, not left UGP ring
75%
Nielsen's semicommutative ring that isn't McCoy
29.0%
Noetherian domain that is not N-1
83%
Noetherian ring that is not Grothendieck and not Nagata
98%
Non-Artinian simple ring
39%
Non-symmetric $2$-primal ring
70%
Nonlocal endomorphism ring of a uniserial module
79%
O'Meara's infinite matrix algebra
42%
Osofsky's $32$ element ring
97%
Osofsky's Type I ring
98%
Page's left-not-right FPF ring
61%
Perfect non-Artinian ring
96%
Perfect ring that isn't semiprimary
85%
Progression free polynomial ring
83%
Pseudo-Frobenius, not quasi-Frobenius ring
90%
Puninski's triangular serial ring
55.0%
Quasi-continuous ring that is not Ikeda-Nakayama
97%
Ram's Ore extension ring
77%
Reversible non-symmetric ring
95%
Right-not-left ACC on annihilators triangular ring
37%
Right-not-left Artinian triangular ring
87%
Right-not-left Kasch ring
86%
Right-not-left Noetherian triangular ring
86%
Right-not-left coherent ring
89%
Right-not-left nonsingular ring
91%
Right-not-left simple injective ring
57.0%
Ring of holomorphic functions on $\mathbb C$
98%
Samuel's UFD having a non-UFD power series ring
96%
Semicommutative $R$ such that $R[x]$ is not semicommutative
26%
Shepherdson's domain that is not stably finite
77%
Simple, connected, Noetherian ring with zero divisors
77%
Simple, non-Artinian, von Neumann regular ring
84%
Small's right hereditary, not-left semihereditary ring
37%
Square of a torch ring
59%
Trivial extension torch ring
77%
Varadarajan's left-not-right coHopfian ring
83%
catenary, not universally catenary
97%
division ring with an antihomomorphism but no involution
99%
field of $p$-adic numbers
100%
non-$h$-local domain
83%
reduced $I_0$ ring that is not exchange
70%
reduced exchange ring which is not semiregular
72%
ring of germs of holomorphic functions on $\mathbb C^n$, $n>1$
97%
Šter's clean ring with non-clean corner rings
70%
Šter's counterexample showing "clean" is not Morita invariant
20%