About: Quasi-Frobenius ring

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In mathematics, especially ring theory, the class of Frobenius rings and their generalizations are the extension of work done on Frobenius algebras. Perhaps the most important generalization is that of quasi-Frobenius rings (QF rings), which are in turn generalized by right pseudo-Frobenius rings (PF rings) and right finitely pseudo-Frobenius rings (FPF rings). Other diverse generalizations of quasi-Frobenius rings include QF-1, QF-2 and QF-3 rings.

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rdf:type	software
rdfs:label	Anneau quasi-Frobenius (fr) 準フロベニウス環 (ja) Quasi-Frobenius ring (en)
rdfs:comment	Un anneau est appelé quasi-Frobenius ou quasi-frobéniusien s'il est artinien et si le dual d'un -module à gauche (resp. à droite) simple est un -module à droite (resp. à gauche) simple. (fr) 数学、とくに環論において、フロベニウス環 (Frobenius ring) のクラスとその一般化は、フロベニウス多元環についてなされた研究の拡張である。おそらく最も重要な一般化は準フロベニウス環 (quasi-Frobenius ring, QF ring) のそれであろう。これはさらに右擬フロベニウス環 (pseudo-Frobenius ring, PF ring) と右有限擬フロベニウス環 (finitely pseudo-Frobenius ring, FPF ring) に一般化される。準フロベニウス環の他の種々の一般化には QF-1, QF-2, QF-3 環がある。これらのタイプの環はゲオルク・フロベニウスによって考察された多元環の子孫と見ることができる。準フロベニウス環のパイオニアたちを部分的に挙げれば、、森田紀一、中山正、, 。 (ja) In mathematics, especially ring theory, the class of Frobenius rings and their generalizations are the extension of work done on Frobenius algebras. Perhaps the most important generalization is that of quasi-Frobenius rings (QF rings), which are in turn generalized by right pseudo-Frobenius rings (PF rings) and right finitely pseudo-Frobenius rings (FPF rings). Other diverse generalizations of quasi-Frobenius rings include QF-1, QF-2 and QF-3 rings. (en)
dcterms:subject	Module theory Ring theory
Wikipage page ID	31557888 (xsd:integer)
Wikipage revision ID	1073583628 (xsd:integer)
Link from a Wikipage to another Wikipage	Robert M. Thrall Module theory Richard Brauer Injective cogenerator Injective hull Injective module Jacobson radical Quotient ring Ring theory Generator (category theory) Noetherian ring Serial module Quasi-Frobenius Lie algebra Morita equivalence Frobenius algebra Tadashi Nakayama (mathematician) Kasch ring Local ring Minimal ideal Faithful module Finitely generated module Balanced module Cecil J. Nesbitt Gorenstein ring Projective module Ring theory Kiiti Morita Artinian ring Socle (mathematics) Free module Semisimple ring Georg Frobenius Semilocal ring Springer-Verlag Essential submodule
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=PswhrD_wUIkC
sameAs	Quasi-Frobenius ring Quasi-Frobenius ring Quasi-Frobenius ring Quasi-Frobenius ring Quasi-Frobenius ring
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:Harvtxt
has abstract	In mathematics, especially ring theory, the class of Frobenius rings and their generalizations are the extension of work done on Frobenius algebras. Perhaps the most important generalization is that of quasi-Frobenius rings (QF rings), which are in turn generalized by right pseudo-Frobenius rings (PF rings) and right finitely pseudo-Frobenius rings (FPF rings). Other diverse generalizations of quasi-Frobenius rings include QF-1, QF-2 and QF-3 rings. These types of rings can be viewed as descendants of algebras examined by Georg Frobenius. A partial list of pioneers in quasi-Frobenius rings includes R. Brauer, K. Morita, T. Nakayama, C. J. Nesbitt, and R. M. Thrall. (en) Un anneau est appelé quasi-Frobenius ou quasi-frobéniusien s'il est artinien et si le dual d'un -module à gauche (resp. à droite) simple est un -module à droite (resp. à gauche) simple. (fr) 数学、とくに環論において、フロベニウス環 (Frobenius ring) のクラスとその一般化は、フロベニウス多元環についてなされた研究の拡張である。おそらく最も重要な一般化は準フロベニウス環 (quasi-Frobenius ring, QF ring) のそれであろう。これはさらに右擬フロベニウス環 (pseudo-Frobenius ring, PF ring) と右有限擬フロベニウス環 (finitely pseudo-Frobenius ring, FPF ring) に一般化される。準フロベニウス環の他の種々の一般化には QF-1, QF-2, QF-3 環がある。これらのタイプの環はゲオルク・フロベニウスによって考察された多元環の子孫と見ることができる。準フロベニウス環のパイオニアたちを部分的に挙げれば、、森田紀一、中山正、, 。 (ja)
gold:hypernym	Extension
prov:wasDerivedFrom	wikipedia-en:Quasi-Frobenius_ring?oldid=1073583628&ns=0
page length (characters) of wiki page	8014 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Quasi-Frobenius_ring
is Link from a Wikipage to another Wikipage of	List of abstract algebra topics Injective module Serial module Quasi-Frobenius Lie algebra Glossary of ring theory Morita equivalence Frobenius algebra Balanced module List of things named after Ferdinand Georg Frobenius
is foaf:primaryTopic of	wikipedia-en:Quasi-Frobenius_ring

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