Ring extension

Ring extension

In mathematics, more specifically in ring theory, a ring extension or extension ring is a ring "R" with a subring "S". We write "R"/"S" and say "R" is a "ring extension" of "S"

Given an extension "R"/"S" of commutative rings and a prime ideal P of "R", it follows thatthe intersection, say p, of P with "S" is a prime ideal of "S". In this case we say that P lies over p. The situation is more complicated when "R" is not commutative.


* A field extension is a special case of ring extension.

See also

* Integral extension
* Group extension
* Algebraic extension
* Ore extension


Wikimedia Foundation. 2010.

Поможем написать курсовую

Look at other dictionaries:

  • Extension (mathematics) — In mathematics, the word extension has many uses. See:Analysis* Carathéodory s extension theorem * Continuous linear extension * M. Riesz extension theorem * Krein extension theorem * Hahn Banach theoremAlgebra* Abelian extension * Algebraic… …   Wikipedia

  • Ring Road (Regina) — Ring Road is a 4 lane controlled access highway in Regina, Saskatchewan, Canada. It is an extension of the Trans Canada Highway that bypasses the city on the north east side. Ring Road has a speed limit of 100km/h (about 62mph) and consists of 7… …   Wikipedia

  • Ring Indicator — Ring Indicator, abbreviated as RI, is a signal that exists inside an RS232 serial communications cable that goes between a computer and a modem. The signal is sent from the modem to the computer, typically over pin 9 of a nine pin (DE9) serial… …   Wikipedia

  • Ring Road, Delhi — This article is about the Inner Ring Road of New Delhi. For the Outer Ring Road, see Outer Ring Road, New Delhi. Delhi features 2 ring roads, a main one and an outer one. The two ring roads have a combined length of 87 km.Delhi s Inner Ring Road… …   Wikipedia

  • Extension and contraction of ideals — In commutative algebra, the extension and contraction of ideals are operations performed on sets of ideals. Extension of an ideal Let A and B be two commutative rings with unity, and let f : A → B be a (unital) ring homomorphism. If mathfrak{a}… …   Wikipedia

  • Extension of scalars — In abstract algebra, extension of scalars is a means of producing a module over a ring S from a module over another ring R, given a homomorphism f : R o S between them. Intuitively, the new module admits multiplication by more scalars than the… …   Wikipedia

  • Ring roads of Beijing — Beijing is one of the very few cities to possess multiple ring roads (or beltways). Among the rarest seen anywhere in a major city in the world is Beijing s 2nd Ring Road, which is extremely central to Tian anmen, the centre of Beijing.1st Ring… …   Wikipedia

  • Ring road — For other uses, see Ring road (disambiguation). Inner ring road of Sheffield, England …   Wikipedia

  • Extension de Thébé — Anneau gossamer L anneau gossamer (littéralement « gaze » en anglais) est un anneau de la planète Jupiter. Sommaire 1 Caractéristiques 2 Voir aussi 2.1 Liens internes 2.2 …   Wikipédia en Français

  • Ring belge N203a — Route nationale 203a (Belgique) Route nationale 203 Contournement de Hal Longueur: 4,1 km Croisements, rond points et sorties …   Wikipédia en Français

Share the article and excerpts

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