login
This site is supported by donations to The OEIS Foundation.

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A027623 a(0) = 1; for n > 0, a(n) = number of rings with n elements. 13
1, 1, 2, 2, 11, 2, 4, 2, 52, 11, 4, 2, 22, 2, 4, 4, 390, 2, 22, 2, 22, 4, 4, 2, 104, 11, 4, 59, 22, 2, 8, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Here a ring means (R,+,*): (R,+) is Abelian group, * is associative, a*(b+c) = a*b+a*c, (a+b)*c = a*c+b*c. Need not contain "1", * need not be commutative.

The paper by Antipkin/Elizarov also gives the number a(p^3) of rings of order p^3. - Hans H. Storrer (storrer(AT)math.unizh.ch), Sep 16 2003

If n is a squared prime, there are 11 mutually nonisomorphic rings of order n [see Raghavendran, p. 228]. - R. J. Mathar, Apr 20 2008

LINKS

Table of n, a(n) for n=0..31.

V. G. Antipkin and V. P. Elizarov, Rings of order p^3, Sib. Math. J. vol 23 no 4 (1982) pp 457-464, MR0668331 (84d:16025)

R. Ballieu [ Math. Rev. 0022841; see also Math. Rev. 51#5655] showed a(8)=52, a(p^3)=3p+50 if p is odd prime.

C. R. Fletcher, Rings of small order, Math. Gaz. vol. 64 (1980) p. 13, 1980, see esp. p. 21.

A. V. Lelechenko, Parity of the number of primes in a given interval and algorithms of the sublinear summation, arXiv preprint arXiv:1305.1639, 2013

C. Noebauer, The Numbers of Small Rings

C. Noebauer, Thesis on the enumeration of near-rings

Christof Noebauer, The Numbers of Small Rings (PostScript).

R. Raghavendran, Finite associative rings, Compositio Mathematica vol 21 no 2 (1969) p 195-229.

Eric Weisstein's World of Mathematics, Ring

EXAMPLE

The 11 rings of order 4 (from Christian G. Bower): over C4: 1*1 = 0, 1 or 2; over C2 X C2 = <1> X <2>: (1*1,1*2,2*1,2*2) = 0000, 0001, 0002, 0012, 0102, 0112, 1002 or 1223.

CROSSREFS

Cf. A037289, A037291.

Sequence in context: A236369 A001038 * A037234 A141651 A213990 A222878

Adjacent sequences:  A027620 A027621 A027622 * A027624 A027625 A027626

KEYWORD

nonn,nice,hard,more,mult

AUTHOR

N. J. A. Sloane, R. K. Guy

EXTENSIONS

More terms from Christian G. Bower, Jun 15 1998. a(16) from Christof Noebauer (christof.noebauer(AT)algebra.uni-linz.ac.at), Sep 29, 2000

Christof Noebauer also reports that the sequence continues a(32) = ? (>18590), a(33) = 4, 4, 4, 121, 2, 4, 4, 104, 2, 8, 2, 22, 22, 4, 2, 780, 11, 22, 4, 22, 2, 118, 4, 104, 4, 4, 2, 44, 2, 4, 22 = a(63), a(64) = ? (> 829826)

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified July 22 09:30 EDT 2014. Contains 244804 sequences.