Transformation of fractions into simple fractions in divisive meadows
arXiv:1510.06233 · doi:10.1016/j.jal.2016.03.001
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.
23 pages; one theorem and two corollaries of it added at end of Sect. 5; some minor errors corrected