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- Principal_ideal_ring abstract "In mathematics, a principal right (left) ideal ring is a ring R in which every right (left) ideal is of the form xR (Rx) for some element x of R. (The right and left ideals of this form, generated by one element, are called principal ideals.) When this is satisfied for both left and right ideals, such as the case when R is a commutative ring, R can be called a principal ideal ring, or simply principal ring.If only the finitely generated right ideals of R are principal, then R is called a right Bézout ring. Left Bézout rings are defined similarly. These conditions are studied in domains as Bézout domains.A commutative principal ideal ring which is also an integral domain is said to be a principal ideal domain (PID). In this article the focus is on the more general concept of a principal ideal ring which is not necessarily a domain.".
- Principal_ideal_ring wikiPageID "6961771".
- Principal_ideal_ring wikiPageLength "7505".
- Principal_ideal_ring wikiPageOutDegree "30".
- Principal_ideal_ring wikiPageRevisionID "694326727".
- Principal_ideal_ring wikiPageWikiLink Artinian_ring.
- Principal_ideal_ring wikiPageWikiLink Automorphism.
- Principal_ideal_ring wikiPageWikiLink Bézout_domain.
- Principal_ideal_ring wikiPageWikiLink Category:Commutative_algebra.
- Principal_ideal_ring wikiPageWikiLink Category:Ring_theory.
- Principal_ideal_ring wikiPageWikiLink Chinese_remainder_theorem.
- Principal_ideal_ring wikiPageWikiLink Commutative_ring.
- Principal_ideal_ring wikiPageWikiLink Dedekind_domain.
- Principal_ideal_ring wikiPageWikiLink Direct_product.
- Principal_ideal_ring wikiPageWikiLink Discrete_valuation_ring.
- Principal_ideal_ring wikiPageWikiLink Division_ring.
- Principal_ideal_ring wikiPageWikiLink Finitely_generated_module.
- Principal_ideal_ring wikiPageWikiLink Idempotent_element.
- Principal_ideal_ring wikiPageWikiLink Integer.
- Principal_ideal_ring wikiPageWikiLink Integral_domain.
- Principal_ideal_ring wikiPageWikiLink Isomorphism_theorem.
- Principal_ideal_ring wikiPageWikiLink Mathematics.
- Principal_ideal_ring wikiPageWikiLink Modular_arithmetic.
- Principal_ideal_ring wikiPageWikiLink Multiplicatively_closed_set.
- Principal_ideal_ring wikiPageWikiLink Noetherian_ring.
- Principal_ideal_ring wikiPageWikiLink Polynomial_ring.
- Principal_ideal_ring wikiPageWikiLink Power_set.
- Principal_ideal_ring wikiPageWikiLink Principal_ideal.
- Principal_ideal_ring wikiPageWikiLink Principal_ideal_domain.
- Principal_ideal_ring wikiPageWikiLink Semisimple_module.
- Principal_ideal_ring wikiPageWikiLink Serial_module.
- Principal_ideal_ring wikiPageWikiLink Springer_Science+Business_Media.
- Principal_ideal_ring wikiPageWikiLink Symmetric_difference.
- Principal_ideal_ring wikiPageWikiLink Thomas_W._Hungerford.
- Principal_ideal_ring wikiPageWikiLink Von_Neumann_regular_ring.
- Principal_ideal_ring wikiPageWikiLinkText "Principal ideal ring".
- Principal_ideal_ring wikiPageWikiLinkText "Principal_ideal_ring#Structure_theory_for_commutative_PIR's".
- Principal_ideal_ring wikiPageWikiLinkText "principal ideal ring".
- Principal_ideal_ring wikiPageWikiLinkText "principal right ideal domain".
- Principal_ideal_ring wikiPageWikiLinkText "principal right ideals".
- Principal_ideal_ring wikiPageWikiLinkText "principal ring".
- Principal_ideal_ring wikiPageWikiLinkText "principal".
- Principal_ideal_ring wikiPageUsesTemplate Template:Citation.
- Principal_ideal_ring wikiPageUsesTemplate Template:Harv.
- Principal_ideal_ring wikiPageUsesTemplate Template:Lang_Algebra.
- Principal_ideal_ring wikiPageUsesTemplate Template:Reflist.
- Principal_ideal_ring subject Category:Commutative_algebra.
- Principal_ideal_ring subject Category:Ring_theory.
- Principal_ideal_ring hypernym R.
- Principal_ideal_ring type Redirect.
- Principal_ideal_ring comment "In mathematics, a principal right (left) ideal ring is a ring R in which every right (left) ideal is of the form xR (Rx) for some element x of R.".
- Principal_ideal_ring label "Principal ideal ring".
- Principal_ideal_ring sameAs Q2905043.
- Principal_ideal_ring sameAs חוג_בזו.
- Principal_ideal_ring sameAs 単項イデアル環.
- Principal_ideal_ring sameAs Pierścień_ideałów_głównych.
- Principal_ideal_ring sameAs m.0gyykm.
- Principal_ideal_ring sameAs Кольцо_главных_идеалов.
- Principal_ideal_ring sameAs Q2905043.
- Principal_ideal_ring sameAs 主理想環.
- Principal_ideal_ring wasDerivedFrom Principal_ideal_ring?oldid=694326727.
- Principal_ideal_ring isPrimaryTopicOf Principal_ideal_ring.