OFFSET
1,4
COMMENTS
A ring without 1 is still a ring, but sometimes it is called a rng, or a non-unital ring, or a pseudo-ring (see Wikipedia links).
LINKS
Wikipedia, Pseudo-ring.
Wikipedia, Rng.
EXAMPLE
a(1) = 0 because the only ring with 1 element is the zero ring with the element 0, and for this ring, 0 and 1 coincide.
a(2) = 1, and for this corresponding ring with elements {0,a}, the multiplication that is defined by: 0*0 = 0*a = a*0 = a*a = 0 is commutative, also this ring is without unit, hence a(2) = 1; the Matrix ring {0,a} with coefficients from Z/2Z:
(0 0) (0 0)
0 = (0 0) a = (1 0) is such an example.
For n=8, there are 52 rings of order 8, 24 of which are commutative rings without 1, so a(8) = 24.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Bernard Schott, Mar 09 2021
STATUS
approved