It looks, like if it is going into the right directions
FiniteField looks good, maybe FiniteRing also available?
Well... don't you have HyperDoc->Browse available?
Sorry, I cannot point you to an online API for AXIOM, but I'm
maintaining an API for FriCAS (which is relatively close.
http://fricas.github.io/
You are probably looking for
http://fricas.github.io/api/IntegerMod.html
What I'm looking for, is polynoms with modulo-coefficients.
Huh? For primes p that's exactly what I've given you. Since then Z_p is
a field.
For non-prime-powers use IntegerMod.