7.2.2 map (plural)
Maps are ring maps from a preimage ring (source) into the basering (target), defined by specifying images for source variables in the target ring.
Maps between rings with different coefficient fields are possible and listed below.
Canonically realized are
Possible are furthermore
Finally, in PLURAL we allow the mapping from rings with coefficient field Q to rings whose ground fields have finite characteristic:
In these cases the denominator and the numerator
of a number are mapped separately by the usual
map from Z to Z/p, and the image of the number
is built again afterwards by division. It is thus
not allowed to map numbers whose denominator is
divisible by the characteristic of the target
ground field, or objects containing such numbers.
We, therefore, strongly recommend to use such
maps only to map objects with integer coefficients.