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- Minimal_ideal abstract "In the branch of abstract algebra known as ring theory, a minimal right ideal of a ring R is a nonzero right ideal which contains no other nonzero right ideal. Likewise a minimal left ideal is a nonzero left ideal of R containing no other nonzero left ideals of R, and a minimal ideal of R is a nonzero ideal containing no other nonzero two-sided ideal of R. (Isaacs 2009, p.190)Said another way, minimal right ideals are minimal elements of the poset of nonzero right ideals of R ordered by inclusion. The reader is cautioned that outside of this context, some posets of ideals may admit the zero ideal, and so zero could potentially be a minimal element in that poset. This is the case for the poset of prime ideals of a ring, which may include the zero ideal as a minimal prime ideal.".
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- Minimal_ideal wikiPageWikiLink Abstract_algebra.
- Minimal_ideal wikiPageWikiLink Artinian_ring.
- Minimal_ideal wikiPageWikiLink Bimodule.
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- Minimal_ideal wikiPageWikiLink Category:Abstract_algebra.
- Minimal_ideal wikiPageWikiLink Category:Ideals.
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- Minimal_ideal wikiPageWikiLink Duality_(mathematics).
- Minimal_ideal wikiPageWikiLink Graduate_Studies_in_Mathematics.
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- Minimal_ideal wikiPageWikiLink Ideal_(ring_theory).
- Minimal_ideal wikiPageWikiLink Idempotent_element.
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- Minimal_ideal wikiPageWikiLink Maximal_ideal.
- Minimal_ideal wikiPageWikiLink Minimal_element.
- Minimal_ideal wikiPageWikiLink Minimal_prime_ideal.
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- Minimal_ideal wikiPageWikiLink Principal_ideal.
- Minimal_ideal wikiPageWikiLink Right_ideal.
- Minimal_ideal wikiPageWikiLink Ring_(mathematics).
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- Minimal_ideal wikiPageWikiLink Simple_ring.
- Minimal_ideal wikiPageWikiLink Socle_(mathematics).
- Minimal_ideal wikiPageWikiLink Springer-Verlag.
- Minimal_ideal wikiPageWikiLink Springer_Science+Business_Media.
- Minimal_ideal wikiPageWikiLinkText "Minimal ideal".
- Minimal_ideal wikiPageWikiLinkText "minimal ideal".
- Minimal_ideal wikiPageWikiLinkText "minimal left ideal".
- Minimal_ideal wikiPageWikiLinkText "minimal left ideals".
- Minimal_ideal wikiPageWikiLinkText "minimal right ideal".
- Minimal_ideal hasPhotoCollection Minimal_ideal.
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- Minimal_ideal subject Category:Abstract_algebra.
- Minimal_ideal subject Category:Ideals.
- Minimal_ideal subject Category:Ring_theory.
- Minimal_ideal hypernym Nonzero.
- Minimal_ideal type Article.
- Minimal_ideal type Article.
- Minimal_ideal comment "In the branch of abstract algebra known as ring theory, a minimal right ideal of a ring R is a nonzero right ideal which contains no other nonzero right ideal. Likewise a minimal left ideal is a nonzero left ideal of R containing no other nonzero left ideals of R, and a minimal ideal of R is a nonzero ideal containing no other nonzero two-sided ideal of R.".
- Minimal_ideal label "Minimal ideal".
- Minimal_ideal sameAs 極小イデアル.
- Minimal_ideal sameAs m.0jt02sg.
- Minimal_ideal sameAs Q17098947.
- Minimal_ideal sameAs Q17098947.
- Minimal_ideal wasDerivedFrom Minimal_ideal?oldid=675189340.
- Minimal_ideal isPrimaryTopicOf Minimal_ideal.