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- Maximal_ideal abstract "In mathematics, more specifically in ring theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other ideals contained between I and R.Maximal ideals are important because the quotient rings of maximal ideals are simple rings, and in the special case of unital commutative rings they are also fields. In noncommutative ring theory, a maximal right ideal is defined analogously as being a maximal element in the poset of proper right ideals, and similarly, a maximal left ideal is defined to be a maximal element of the poset of proper left ideals. Since a one sided maximal ideal A is not necessarily two-sided, the quotient R/A is not necessarily a ring, but it is a simple module over R. If R has a unique maximal right ideal, then R is known as a local ring, and the maximal right ideal is also the unique maximal left and unique maximal two-sided ideal of the ring, and is in fact the Jacobson radical J(R). It is possible for a ring to have a unique maximal ideal and yet lack unique maximal one sided ideals: for example, in the ring of 2 by 2 square matrices over a field, the zero ideal is a maximal ideal, but there are many maximal right ideals.".
- Maximal_ideal wikiPageID "48164".
- Maximal_ideal wikiPageRevisionID "603342734".
- Maximal_ideal hasPhotoCollection Maximal_ideal.
- Maximal_ideal subject Category:Ideals.
- Maximal_ideal subject Category:Prime_ideals.
- Maximal_ideal subject Category:Ring_theory.
- Maximal_ideal type Abstraction100002137.
- Maximal_ideal type Cognition100023271.
- Maximal_ideal type Content105809192.
- Maximal_ideal type Idea105833840.
- Maximal_ideal type Ideal105923696.
- Maximal_ideal type Ideals.
- Maximal_ideal type PrimeIdeals.
- Maximal_ideal type PsychologicalFeature100023100.
- Maximal_ideal comment "In mathematics, more specifically in ring theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other ideals contained between I and R.Maximal ideals are important because the quotient rings of maximal ideals are simple rings, and in the special case of unital commutative rings they are also fields.".
- Maximal_ideal label "Ideale massimale".
- Maximal_ideal label "Ideał maksymalny".
- Maximal_ideal label "Idéal maximal".
- Maximal_ideal label "Maximal ideal".
- Maximal_ideal label "Maximales Ideal".
- Maximal_ideal label "Максимальный идеал".
- Maximal_ideal sameAs Maximální_ideál_(teorie_okruhů).
- Maximal_ideal sameAs Maximales_Ideal.
- Maximal_ideal sameAs Idéal_maximal.
- Maximal_ideal sameAs Ideale_massimale.
- Maximal_ideal sameAs 극대_아이디얼.
- Maximal_ideal sameAs Ideał_maksymalny.
- Maximal_ideal sameAs m.0cx9d.
- Maximal_ideal sameAs Q1203540.
- Maximal_ideal sameAs Q1203540.
- Maximal_ideal sameAs Maximal_ideal.
- Maximal_ideal wasDerivedFrom Maximal_ideal?oldid=603342734.
- Maximal_ideal isPrimaryTopicOf Maximal_ideal.