Fractions in Transrational Arithmetic - Bergstra, Jan Aldert (Transmathematica, 2020)
In transrational arithmetic each closed fraction may be written as a simple fraction. It is shown that unlike in involutive meadows, in transrational arithmetic open fractions cannot be written as a sum of simple fractions (i.e. fractions the numerator and denominator of which are polynomials). It is also not the case that each open fraction with a single variable can be written as a mixed fraction.