Transformation of fractions into simple fractions in divisive meadows
J. A. Bergstra, C. A. Middelburg
TL;DR
This paper explores conditions under which fractions in divisive meadows can be transformed into simple fractions without nested fractions, contributing to the understanding of algebraic properties of these structures.
Contribution
It introduces criteria for divisive meadows that allow the transformation of fractions into simple fractions, advancing the algebraic theory of meadows.
Findings
Identifies divisive meadows where fractions can be simplified
Provides a characterization of simple fraction transformation
Enhances understanding of algebraic properties of divisive meadows
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.