Abstract
Meadows are alternatives for fields with a purely equational
axiomatization.
At the basis of meadows lies the decision to make the multiplicative
inverse operation total by imposing that the multiplicative inverse of
zero is zero.
Divisive meadows are meadows with the multiplicative inverse operation
replaced by a division operation.
Viewing a fraction as a term over the signature of divisive meadows that is of the form p / q, we investigate which divisive meadows admit transformation of fractions into simple fractions, i.e. fractions
without proper subterms that are fractions.
Preprint available:
arXiv:1510.06233 [math.RA]