About: Semiprime ring

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In ring theory, a branch of mathematics, semiprime ideals and semiprime rings are generalizations of prime ideals and prime rings. In commutative algebra, semiprime ideals are also called radical ideals and semiprime rings are the same as reduced rings. For example, in the ring of integers, the semiprime ideals are the zero ideal, along with those ideals of the form where n is a square-free integer. So, is a semiprime ideal of the integers (because 30 = 2 × 3 × 5, with no repeated prime factors), but is not (because 12 = 22 × 3, with a repeated prime factor).

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rdfs:label	Semiprimideal (de) 半素環 (ja) 반소환 (ko) Semiprime ring (en)
rdfs:comment	Ein Semiprimideal ist ein Begriff aus der abstrakten Algebra. Er stellt eine Erweiterung des Begriffs des Primideals dar. (de) 数学の一分野である環論において、半素イデアルと半素環は素イデアルと素環の一般化である。可換環論においては、半素イデアルは根基イデアルとも呼ばれる。例えば、有理整数環において、半素イデアルは、零イデアルと、n を square-free な整数としての形のイデアルである。したがって、は有理整数環の半素イデアルだがは半素イデアルでない。半素環のクラスは半原始環、素環、被約環を含む。この記事における多くの定義や主張はとにある。 (ja) 환론에서 반소환(半素環, 영어: semiprime ring)은 멱영 아이디얼이 영 아이디얼 밖에 없는 환이다. 축소환과 소환의 공통적인 일반화이다. (ko) In ring theory, a branch of mathematics, semiprime ideals and semiprime rings are generalizations of prime ideals and prime rings. In commutative algebra, semiprime ideals are also called radical ideals and semiprime rings are the same as reduced rings. For example, in the ring of integers, the semiprime ideals are the zero ideal, along with those ideals of the form where n is a square-free integer. So, is a semiprime ideal of the integers (because 30 = 2 × 3 × 5, with no repeated prime factors), but is not (because 12 = 22 × 3, with a repeated prime factor). (en)
foaf:depiction
dcterms:subject	Ideals (ring theory) Ring theory
Wikipage page ID	7739701 (xsd:integer)
Wikipage revision ID	1068090670 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime ideal Prime ring Ideals (ring theory) Artin–Wedderburn theorem Ring theory Nilradical of a ring Ore condition Annihilator (ring theory) Commutative algebra Ideal (ring theory) Goldie's theorem Graduate Texts in Mathematics Primary ideal Radical of an ideal Ring (mathematics) Ring theory Artinian ring Ascending chain condition Square-free integer Integers Reduced ring Uniform module Semiprimitive ring Semisimple module Springer-Verlag Radical ideal
Link from a Wikipage to an external page	http://planetmath.org/encyclopedia/SemiprimeIdeal.html
sameAs	Semiprime ring Semiprime ring Semiprime ring Semiprime ring Semiprime ring Semiprime ring Semiprime ring Semiprime ring Semiprime ring
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thumbnail	wiki-commons:Special:FilePath/A_portion_of_the_lattice_of_ideals_of_Z_illustrating_prime,_semiprime_and_primary_ideals_SVG.svg?width=300
has abstract	Ein Semiprimideal ist ein Begriff aus der abstrakten Algebra. Er stellt eine Erweiterung des Begriffs des Primideals dar. (de) In ring theory, a branch of mathematics, semiprime ideals and semiprime rings are generalizations of prime ideals and prime rings. In commutative algebra, semiprime ideals are also called radical ideals and semiprime rings are the same as reduced rings. For example, in the ring of integers, the semiprime ideals are the zero ideal, along with those ideals of the form where n is a square-free integer. So, is a semiprime ideal of the integers (because 30 = 2 × 3 × 5, with no repeated prime factors), but is not (because 12 = 22 × 3, with a repeated prime factor). The class of semiprime rings includes semiprimitive rings, prime rings and reduced rings. Most definitions and assertions in this article appear in and. (en) 数学の一分野である環論において、半素イデアルと半素環は素イデアルと素環の一般化である。可換環論においては、半素イデアルは根基イデアルとも呼ばれる。例えば、有理整数環において、半素イデアルは、零イデアルと、n を square-free な整数としての形のイデアルである。したがって、は有理整数環の半素イデアルだがは半素イデアルでない。半素環のクラスは半原始環、素環、被約環を含む。この記事における多くの定義や主張はとにある。 (ja) 환론에서 반소환(半素環, 영어: semiprime ring)은 멱영 아이디얼이 영 아이디얼 밖에 없는 환이다. 축소환과 소환의 공통적인 일반화이다. (ko)
prov:wasDerivedFrom	wikipedia-en:Semiprime_ring?oldid=1068090670&ns=0
page length (characters) of wiki page	6336 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Semiprime_ring
is Link from a Wikipage to another Wikipage of	List of abstract algebra topics Reinhold Baer Levitzky's theorem Glossary of ring theory Morita equivalence Ideal (ring theory) Minimal ideal Noncommutative ring Goldie's theorem Radical of an ideal Regular ideal Mathematical n system N-system (ring theory) Semiprime ideal
is Wikipage redirect of	Mathematical n system N-system (ring theory) Semiprime ideal
is foaf:primaryTopic of	wikipedia-en:Semiprime_ring

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