Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Integral_element> ?p ?o. }
Showing items 1 to 28 of
28
with 100 items per page.
- Integral_element abstract "In commutative algebra, an element b of a commutative ring B is said to be integral over A, a subring of B, if there is an n ≥ 1 and such thatThat is to say, b is a root of a monic polynomial over A. If every element of B is integral over A, then it is said that B is integral over A, or equivalently B is an integral extension of A.If A, B are fields, then the notions of "integral over" and of an "integral extension" are precisely "algebraic over" and "algebraic extensions" in field theory (since the root of any polynomial is the root of a monic polynomial). The special case of greatest interest in number theory is that of complex numbers integral over Z; in this context, they are usually called algebraic integers (e.g., ). The algebraic integers in a finite extension field k of the rationals Q form a subring of k, called the ring of integers of k, a central object in algebraic number theory.The set of elements of B that are integral over A is called the integral closure of A in B. It is a subring of B containing A.In this article, the term ring will be understood to mean commutative ring with a unity.".
- Integral_element wikiPageExternalLink index.html.
- Integral_element wikiPageExternalLink trieste.pdf.
- Integral_element wikiPageExternalLink math.
- Integral_element wikiPageID "9478630".
- Integral_element wikiPageRevisionID "605908553".
- Integral_element hasPhotoCollection Integral_element.
- Integral_element subject Category:Algebraic_structures.
- Integral_element subject Category:Commutative_algebra.
- Integral_element subject Category:Ring_theory.
- Integral_element comment "In commutative algebra, an element b of a commutative ring B is said to be integral over A, a subring of B, if there is an n ≥ 1 and such thatThat is to say, b is a root of a monic polynomial over A.".
- Integral_element label "Estensione intera".
- Integral_element label "Ganzes Element".
- Integral_element label "Integral element".
- Integral_element label "Integraliteit (algebra)".
- Integral_element label "Élément entier".
- Integral_element label "Целый элемент".
- Integral_element label "整性".
- Integral_element sameAs Celistvý_prvek.
- Integral_element sameAs Ganzes_Element.
- Integral_element sameAs Élément_entier.
- Integral_element sameAs Estensione_intera.
- Integral_element sameAs Integraliteit_(algebra).
- Integral_element sameAs m.028bgtz.
- Integral_element sameAs Q1493740.
- Integral_element sameAs Q1493740.
- Integral_element wasDerivedFrom Integral_element?oldid=605908553.
- Integral_element isPrimaryTopicOf Integral_element.