Dear categorists, I have no idea where to ask the following algebra question. Hoping that some of you are algebraists, I am asking it here. I am looking for examples of small (finite and with few elements, say up to 8) commutative semirings with unit, by which I mean an algebraic structure which has +, *, 0 and 1, both operations are commutative and * distributes over +. The initial such structure are the natural numbers. Here are the examples I know: 1) Modular arithmetic, i.e., (Z_n, +, *, 0, 1) 2) Distributive lattices with 0 and 1. 3) "Cut-off" semiring, in which we compute like with natural numbers, but if a value exceeds a given constant N, then we cut it off at N. For example, if N = 7 then we would have 3 + 3 = 6, 3 + 6 = 7, 4 * 4 = 7, etc. Do such semirings have a name? There must be a census of small commutative rings, or even semirings. Does anyone know? Andrej