Division by zero in common meadows
Jan Aldert Bergstra, Alban Ponse · Data Archiving and Networked Services (DANS) · 2014
Common meadows are fields expanded with a total inverse function. Division by zero produces an additional value denoted with "a" that propagates through all operations of the meadow signature (this additional value can be interpreted as an error element). We provide a basis theorem for so-called common cancellation meadows of characteristic zero, that is, common meadows of characteristic zero that admit a certain cancellation law.