division ring
A ring with 0 ≠ 1, such that every non-zero element a has a multiplicative inverse, meaning an element x with ax = xa = 1.

Wikipedia foundation.

Look at other dictionaries:

  • Division ring — In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a non trivial ring in which every non zero element a has a multiplicative inverse, i.e., an element x with a·x = x·a = 1 …   Wikipedia

  • division ring — Math. a ring in which the set of nonzero elements is a group with the operation of multiplication. * * * …   Universalium

  • division ring — (Mathematics) is a ring in which every nonzero element has a multiplicative inverse but multiplication is not necessarily commutative (abstract algebra) …   English contemporary dictionary

  • division ring — Math. a ring in which the set of nonzero elements is a group with the operation of multiplication …   Useful english dictionary

  • Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

  • Division by zero — This article is about the mathematical concept. For other uses, see Division by zero (disambiguation). The function y = 1/x. As x approaches 0 from the right, y approaches infinity. As x approaches 0 from the left, y approaches negative …   Wikipedia

  • Division algebra — In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field, in which division is possible. Contents 1 Definitions 2 Associative division algebras 3 Not necessarily asso …   Wikipedia

  • Ring Magazine Light Heavyweight Champion — The Ring Magazine Light Heavyweight belt is issued by Ring Magazine to the top man in the division. The holder of a Ring Magazine belt is usually considered the undisputed world champion. Unlike the numerous alphabet belts (WBA, WBC, IBF, WBO… …   Wikipedia

  • Division De Huygens — La division de Huygens est un espace situé à l intérieur du système des anneaux de la planète Saturne. Sommaire 1 Caractéristiques 2 Voir aussi 2.1 Liens internes 2.2 …   Wikipédia en Français

  • Division Huygens — Division de Huygens La division de Huygens est un espace situé à l intérieur du système des anneaux de la planète Saturne. Sommaire 1 Caractéristiques 2 Voir aussi 2.1 Liens internes 2.2 …   Wikipédia en Français

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”