ISO example of a concrete "non-arithmetic" ring





I know of examples of groups that can be readily understood by a
lay person without requiring any use of numbers and arithmetic
(e.g. the group of permutations of a finite set). But I can't
think of any "non-arithmetic" examples of rings. Does anyone know
of one?

(This is strictly for my own edification. It seems to me that the
notion of a ring is a fundamentally arithmetic construct; i.e.
without arithmetic rules of combination, one has no rings. Is this
impression correct?)

Thanks!

kj

--
NOTE: In my address everything before the first period is backwards;
and the last period, and everything after it, should be discarded.
.

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