ordered ring

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• Ordered ring — In abstract algebra, an ordered ring is a commutative ring R with a total order ≤ such that for all a, b, and c in R: if a ≤ b then a + c ≤ b + c. if 0 ≤ a and 0 ≤ b then 0 ≤ ab. Ordered rings are familiar from arithmetic. Examples include the… …   Wikipedia

• Ordered field — In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations. Historically, the axiomatization of an ordered field was abstracted gradually from the real numbers, by… …   Wikipedia

• 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

• Ring-tailed Lemur — Taxobox name = Ring tailed LemurMSW3 Groves|pages=117|id=12100056] status = NT trend = down status system = iucn3.1 status ref = regnum = Animalia phylum = Chordata classis = Mammalia ordo = Primates familia = Lemuridae genus = Lemur genus… …   Wikipedia

• Ring Raiders — Articleissues citations missing = August 2008 refimprove = August 2008Infobox Television show name = Ring Raiders caption = format = Animated creator = DIC Entertainment Those Characters from Cleveland writer = Phil Harnage voices = Dan Gilvezan… …   Wikipedia

• Ring ni Kakero — Infobox animanga/Header name = Ring ni Kakero caption = ja name = リングにかけろ ja name trans = genre = Sports (Boxing)Infobox animanga/Manga title = author = Masami Kurumada publisher = flagicon|Japan Shueisha publisher other = demographic = Shōnen… …   Wikipedia

• Partially-ordered group — In abstract algebra, a partially ordered group is a group (G,+) equipped with a partial order ≤ that is translation invariant; in other words, ≤ has the property that, for all a, b, and g in G, if a ≤ b then a+g ≤ b+g and g+a ≤ g+b. An element x… …   Wikipedia

• Valuation ring — In abstract algebra, a valuation ring is an integral domain D such that for every element x of its field of fractions F , at least one of x or x 1 belongs to D .Given a field F , if D is a subring of F such that either x or x 1 belongs to D for… …   Wikipedia

• Duquesne Spy Ring — The 33 convicted members of the Duquesne spy ring (FBI print). The Duquesne Spy Ring is the largest espionage case in United States history that ended in convictions. A total of thirty three members of a German espionage network headed by… …   Wikipedia

• War of the Ring — Infobox Me battle date = 3018 − 3019 Third Age place = Northwestern Middle earth result= Free peoples victory; destruction of Sauron; Arnor and Gondor reunited books = The Lord of the Rings , Unfinished Tales participants = See combatant1 = Free… …   Wikipedia

• Small ring (Brussels) — The Brussels small ring ( fr. petite ceinture, nl. Kleine Ring) or inner ring road is a series of roadways in central Brussels surrounding the historic city centre. It was built on the site of the Brussels s second set of walls, built in the 16th …   Wikipedia