ترغب بنشر مسار تعليمي؟ اضغط هنا

Transformation of fractions into simple fractions in divisive meadows

172   0   0.0 ( 0 )
 نشر من قبل Kees Middelburg
 تاريخ النشر 2015
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

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.


قيم البحث

اقرأ أيضاً

Univariate fractions can be transformed to mixed fractions in the equational theory of meadows of characteristic zero.
A meadow is a zero totalised field (0^{-1}=0), and a cancellation meadow is a meadow without proper zero divisors. In this paper we consider differential meadows, i.e., meadows equipped with differentiation operators. We give an equational axiomatiza tion of these operators and thus obtain a finite basis for differential cancellation meadows. Using the Zariski topology we prove the existence of a differential cancellation meadow.
Meadows - commutative rings equipped with a total inversion operation - can be axiomatized by purely equational means. We study subvarieties of the variety of meadows obtained by extending the equational theory and expanding the signature.
Meadows have been proposed as 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. T hus, the multiplicative inverse operation of a meadow is an involution. In this paper, we study `non-involutive meadows, i.e. variants of meadows in which the multiplicative inverse of zero is not zero, and pay special attention to non-involutive meadows in which the multiplicative inverse of zero is one.
We consider the signatures $Sigma_m=(0,1,-,+, cdot, ^{-1})$ of meadows and $(Sigma_m, {mathbf s})$ of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom scheme expressing formal realness; the second axiomatization presupposes an ordering. We apply these completeness results in order to obtain complete axiomatizations of the complex numbers.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا