2015 | OriginalPaper | Buchkapitel
Division by Zero in Common Meadows
Autoren: Jan A. Bergstra, Alban Ponse
Verlag: Springer International Publishing
Common meadows are fields expanded with a total multiplicative inverse function. Division by zero produces an additional value denoted with “
${\textup{\textbf{a}}}$
” 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.
