Transformation of Fractions into Simple Fractions in Divisive Meadows

This is to announce a new version of an electronic preprint concerning meadows. The preprint “Transformation of fractions into simple fractions in divisive meadows” has now been updated (arXiv:1510.06233v3 [math.RA]). In this preprint, it is investigated which divisive meadows admit transformation of fractions into simple fractions, i.e. fractions whose numerator and denominator do not contain fractions.

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Fracpairs and Fractions over a Reduced Commutative Ring

This is to announce a new version of an electronic preprint concerning an application of meadows. The preprint “Fracpairs and Fractions over a Reduced Commutative Ring” has now been replaced by a substantial revision (arXiv:1411.4410v2 [math.RA]). In this preprint, the principle of fractions as pairs is elaborated in case denominators may be zero. The resulting mathematical structure is essentially that of a common meadow.

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A Negative Result on Algebraic Specifications of the Meadow of Rational Numbers

This is to announce a new version of an electronic preprint concerning meadows. The preprint “A Negative Result on Algebraic Specifications of the Meadow of Rational Numbers” has now been updated (arXiv:1507.00548v2 [math.RA]). In this preprint, it is investigated whether there exists a logically weakest initial algebra specification of the meadow of rational numbers.

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Probabilistic Thread Algebra

This is to announce the publication of a paper concerning an application of meadows. The paper “Probabilistic Thread Algebra” (doi:10.7561/SACS.2015.2.211) has now been published. This paper introduce an algebraic theory of mathematical objects that represent the behaviours produced by probabilistic instruction sequences under execution. It concerns an application of meadows because functions whose range is the carrier of a meadow are taken as probability measures.

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