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- Balanced_module abstract "In the subfield of abstract algebra known as module theory, a right R module M is called a balanced module (or is said to have the double centralizer property) if every endomorphism of the abelian group M which commutes with all R-endomorphisms of M is given by multiplication by a ring element. Explicitly, for any additive endomorphism f, if fg = gf for every R endomorphism g, then there exists an r in R such that f(x) = xr for all x in M. In the case of non-balanced modules, there will be such an f that is not expressible this way.In the language of centralizers, a balanced module is one satisfying the conclusion of the double centralizer theorem, that is, the only endomorphisms of the group M commuting with all the R endomorphisms of M are the ones induced by right multiplication by ring elements.A ring is called balanced if every right R module is balanced. It turns out that being balanced is a left-right symmetric condition on rings, and so there is no need to prefix it with "left" or "right".The study of balanced modules and rings is an outgrowth of the study of QF-1 rings by C.J. Nesbitt and R. M. Thrall. This study was continued in V. P. Camillo's dissertation, and later it became fully developed. The paper (Dlab & Ringel 1972) gives a particularly broad view with many examples. In addition to these references, K. Morita and H. Tachikawa have also contributed published and unpublished results. A partial list of authors contributing to the theory of balanced modules and rings can be found in the references.".
- Balanced_module wikiPageID "34302118".
- Balanced_module wikiPageLength "5746".
- Balanced_module wikiPageOutDegree "24".
- Balanced_module wikiPageRevisionID "608549233".
- Balanced_module wikiPageWikiLink Abstract_algebra.
- Balanced_module wikiPageWikiLink Annihilator_(ring_theory).
- Balanced_module wikiPageWikiLink Category:Module_theory.
- Balanced_module wikiPageWikiLink Category:Ring_theory.
- Balanced_module wikiPageWikiLink Cecil_J._Nesbitt.
- Balanced_module wikiPageWikiLink Center_(algebra).
- Balanced_module wikiPageWikiLink Center_of_a_ring.
- Balanced_module wikiPageWikiLink Double_centralizer_theorem.
- Balanced_module wikiPageWikiLink Endomorphism.
- Balanced_module wikiPageWikiLink Faithful_module.
- Balanced_module wikiPageWikiLink Finitely_generated_module.
- Balanced_module wikiPageWikiLink Hiroyuki_Tachikawa.
- Balanced_module wikiPageWikiLink Ideal_(ring_theory).
- Balanced_module wikiPageWikiLink Kiiti_Morita.
- Balanced_module wikiPageWikiLink Module_(mathematics).
- Balanced_module wikiPageWikiLink Module_theory.
- Balanced_module wikiPageWikiLink Morita_equivalence.
- Balanced_module wikiPageWikiLink Quasi-Frobenius_ring.
- Balanced_module wikiPageWikiLink Robert_M._Thrall.
- Balanced_module wikiPageWikiLink Serial_module.
- Balanced_module wikiPageWikiLink Simple_module.
- Balanced_module wikiPageWikiLink Simple_ring.
- Balanced_module wikiPageWikiLink Uniserial_ring.
- Balanced_module wikiPageWikiLink Victor_P._Camillo.
- Balanced_module wikiPageWikiLinkText "balanced module".
- Balanced_module wikiPageWikiLinkText "double centralizer property".
- Balanced_module hasPhotoCollection Balanced_module.
- Balanced_module wikiPageUsesTemplate Template:Citation.
- Balanced_module wikiPageUsesTemplate Template:Harv.
- Balanced_module wikiPageUsesTemplate Template:Reflist.
- Balanced_module wikiPageUsesTemplate Template:Sfn.
- Balanced_module subject Category:Module_theory.
- Balanced_module subject Category:Ring_theory.
- Balanced_module comment "In the subfield of abstract algebra known as module theory, a right R module M is called a balanced module (or is said to have the double centralizer property) if every endomorphism of the abelian group M which commutes with all R-endomorphisms of M is given by multiplication by a ring element. Explicitly, for any additive endomorphism f, if fg = gf for every R endomorphism g, then there exists an r in R such that f(x) = xr for all x in M.".
- Balanced_module label "Balanced module".
- Balanced_module sameAs m.0hzrmkk.
- Balanced_module sameAs Q4849994.
- Balanced_module sameAs Q4849994.
- Balanced_module wasDerivedFrom Balanced_module?oldid=608549233.
- Balanced_module isPrimaryTopicOf Balanced_module.