About: Nil ideal

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In mathematics, more specifically ring theory, a left, right or two-sided ideal of a ring is said to be a nil ideal if each of its elements is nilpotent. The nilradical of a commutative ring is an example of a nil ideal; in fact, it is the ideal of the ring maximal with respect to the property of being nil. Unfortunately the set of nil elements does not always form an ideal for noncommutative rings. Nil ideals are still associated with interesting open questions, especially the unsolved Köthe conjecture.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Cognition100023271 yago:Content105809192 yago:Idea105833840 yago:Ideal105923696 yago:PsychologicalFeature100023100 yago:WikicatIdeals
rdfs:label	Nilideal (de) Nil ideal (en) Ideal nil (pt) Ніль-ідеал (uk)
rdfs:comment	Nilideal ist ein mathematischer Begriff aus der Ringtheorie. (de) In mathematics, more specifically ring theory, a left, right or two-sided ideal of a ring is said to be a nil ideal if each of its elements is nilpotent. The nilradical of a commutative ring is an example of a nil ideal; in fact, it is the ideal of the ring maximal with respect to the property of being nil. Unfortunately the set of nil elements does not always form an ideal for noncommutative rings. Nil ideals are still associated with interesting open questions, especially the unsolved Köthe conjecture. (en) Em matemática, mais precisamente na teoria de anéis, um ideal de um anel é um ideal nil se todos os seus elementos forem nilpotentes. O de um anel comutativo é um exemplo de ideal nil; de fato, ele é o ideal maximal do anel em relação à propriedade de ser nil. Apesar deste exemplo, a teoria de ideais nil é mais interessante no caso dos , em que vários problemas ainda permanecem elusivos—por exemplo, a . (pt) У теорії кілець, лівий, правий або двосторонній ідеал I кільця R називається ніль-ідеалом якщо всі його елементи нільпотентними, тобто для кожного існує натуральне число n для якого Якщо всі елементи кільця є нільпотентними (це можливо лише для кілець без одиниці), то кільце називають ніль-кільцем. (uk)
dct:subject	Ideals (ring theory)
Wikipage page ID	3100140 (xsd:integer)
Wikipage revision ID	1067025486 (xsd:integer)
Link from a Wikipage to another Wikipage	Ideals (ring theory) Right-Noetherian ring Jacobson radical Köthe conjecture Levitzky's theorem Mathematics Nilradical of a ring Commutative ring Ideal (ring theory) Nilpotent ideal Nilpotent element Noncommutative ring Ring (mathematics) Ring theory Artinian ring European Mathematical Society Nil ring
Link from a Wikipage to an external page	http://www.icm2006.org/proceedings/Vol_II/contents/ICM_Vol_2_12.pdf
sameAs	Nil ideal Nil ideal Nil ideal Nil ideal Nil ideal Nil ideal Nil ideal Nil ideal
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:Reflist dbt:Sfn
has abstract	Nilideal ist ein mathematischer Begriff aus der Ringtheorie. (de) In mathematics, more specifically ring theory, a left, right or two-sided ideal of a ring is said to be a nil ideal if each of its elements is nilpotent. The nilradical of a commutative ring is an example of a nil ideal; in fact, it is the ideal of the ring maximal with respect to the property of being nil. Unfortunately the set of nil elements does not always form an ideal for noncommutative rings. Nil ideals are still associated with interesting open questions, especially the unsolved Köthe conjecture. (en) Em matemática, mais precisamente na teoria de anéis, um ideal de um anel é um ideal nil se todos os seus elementos forem nilpotentes. O de um anel comutativo é um exemplo de ideal nil; de fato, ele é o ideal maximal do anel em relação à propriedade de ser nil. Apesar deste exemplo, a teoria de ideais nil é mais interessante no caso dos , em que vários problemas ainda permanecem elusivos—por exemplo, a . (pt) У теорії кілець, лівий, правий або двосторонній ідеал I кільця R називається ніль-ідеалом якщо всі його елементи нільпотентними, тобто для кожного існує натуральне число n для якого Якщо всі елементи кільця є нільпотентними (це можливо лише для кілець без одиниці), то кільце називають ніль-кільцем. (uk)
gold:hypernym	Nilpotent
prov:wasDerivedFrom	wikipedia-en:Nil_ideal?oldid=1067025486&ns=0
page length (characters) of wiki page	4899 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Nil_ideal
is Link from a Wikipage to another Wikipage of	Jacobson radical Kurosh problem Köthe conjecture Levitzky's theorem Nil Glossary of ring theory Nilpotent Ideal (ring theory) Idempotent (ring theory) Nilpotent ideal Agata Smoktunowicz Goldie's theorem Radical of a ring List of unsolved problems in mathematics SBI ring Zorn ring
is Wikipage disambiguates of	Nil
is foaf:primaryTopic of	wikipedia-en:Nil_ideal

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