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ISBN: 0511565704 Year: 1975 Publisher: Cambridge : Cambridge University Press,
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This work specifically surveys simple Noetherian rings. The authors present theorems on the structure of simple right Noetherian rings and, more generally, on simple rings containing a uniform right ideal U. The text is as elementary and self-contained as practicable, and the little background required in homological and categorical algebra is given in a short appendix. Full definitions are given and short, complete, elementary proofs are provided for such key theorems as the Morita theorem, the Correspondence theorem, the Wedderburn-Artin theorem, the Goldie-Lesieur-Croisot theorem, and many others. Complex mathematical machinery has been eliminated wherever possible or its introduction into the text delayed as long as possible. (Even tensor products are not required until Chapter 3.)
Book
ISBN: 1470420848 Year: 2001 Publisher: Providence, Rhode Island : American Mathematical Society,
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ISBN: 0470213914 9780470213919 0853129274 9780853129271 Year: 1989 Publisher: Chichester: Ellis Horwood,
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ISBN: 0521836875 0521545374 0511211929 9780511211928 9780521836876 9780521545372 0511217293 9780511217296 0511215509 9780511215506 9780511841699 0511841698 1107161584 9781107161580 1280540672 9781280540677 9786610540679 6610540675 0511315880 9780511315886 0511213697 9780511213694 Year: 2004 Publisher: Cambridge, U.K. New York Cambridge University Press
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This 2004 introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. Various important settings, such as group algebras, Lie algebras, and quantum groups, are sketched at the outset to describe typical problems and provide motivation. The text then develops and illustrates the standard ingredients of the theory: e.g., skew polynomial rings, rings of fractions, bimodules, Krull dimension, linked prime ideals. Recurring emphasis is placed on prime ideals, which play a central role in applications to representation theory. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. Material includes the basic types of quantum groups, which then serve as test cases for the theory developed.
Noetherian rings. --- Noncommutative rings. --- Non-commutative rings --- Associative rings --- Rings, Noetherian --- Commutative rings
Book
ISBN: 1139884212 1107366216 1107370949 1107361303 1107370078 1299404014 1107363756 0511661932 9781107361300 9780511661938 0521317134 9780521317139 Year: 1986 Publisher: Cambridge [Cambridgeshire] New York Cambridge University Press
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This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings. The author focuses on two important aspects: localization and the structure of infective modules. The former is presented in the opening chapters after which some new module-theoretic concepts and methods are used to formulate a new view of localization. This view, which is one of the book's highlights, shows that the study of localization is inextricably linked to the study of certain injectives and leads, for the first time, to some genuine applications of localization in the study of Noetherian rings. In the last part Professor Jategaonkar introduces a unified setting for four intensively studied classes of Noetherian rings: HNP rings, PI rings, enveloping algebras of solvable Lie algebras, and group rings of polycyclic groups. Some appendices summarize relevant background information about these four classes.
Noetherian rings. --- Localization theory. --- Categories (Mathematics) --- Homotopy theory --- Nilpotent groups --- Rings, Noetherian --- Associative rings --- Commutative rings
ISBN: 0821837389 Year: 2005 Publisher: Providence (R.I.) American Mathematical Society
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Ordered algebraic structures --- Noetherian rings. --- Rings (Algebra) --- Anneaux noethériens --- Anneaux (algèbre) --- Noetherian rings --- Representations of rings (Algebra) --- Rings, Noetherian --- Associative rings --- Commutative rings --- Anneaux noethériens.
ISBN: 0821815253 Year: 1987 Publisher: Providence (R.I.): American Mathematical Society
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Lie algebras --- Noetherian rings --- Universal enveloping algebras --- Congresses
ISSN: 00659266 ISBN: 0821805444 Year: 1997 Publisher: Providence (R.I.): American Mathematical Society
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Ordered algebraic structures --- Noetherian rings. --- Semigroups. --- Ideals (Algebra) --- Anneaux noethériens --- Semigroupes --- Idéaux (algèbre) --- Noetherian rings --- Semigroups --- Group theory --- Rings, Noetherian --- Associative rings --- Commutative rings --- Algebraic ideals --- Algebraic fields --- Rings (Algebra) --- Anneaux noethériens. --- Semigroupes.
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ISBN: 0521207347 9780521207348 9780511565700 9780521092999 Year: 1975 Volume: 69 Publisher: Cambridge Cambridge University press
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Ordered algebraic structures --- Noetherian rings --- 512.552 --- #KOPO:Prof. R. Holvoet --- Rings, Noetherian --- Associative rings --- Commutative rings --- Associative rings and algebras --- Noetherian rings. --- 512.552 Associative rings and algebras --- Anneaux noethériens. --- Algèbres commutatives --- Algèbres commutatives --- Anneaux noethériens.
Book
ISBN: 9783031222924 Year: 2023 Publisher: Cham Springer International Publishing :Imprint: Birkhäuser
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This monograph provides an exhaustive treatment of several classes of Noetherian rings and morphisms of Noetherian local rings. Chapters carefully examine some of the most important topics in the area, including Nagata, F-finite and excellent rings, Bertini’s Theorem, and Cohen factorizations. Of particular interest is the presentation of Popescu’s Theorem on Neron Desingularization and the structure of regular morphisms, with a complete proof. Classes of Good Noetherian Rings will be an invaluable resource for researchers in commutative algebra, algebraic and arithmetic geometry, and number theory.
Commutative algebra. --- Commutative rings. --- Commutative Rings and Algebras. --- Rings (Algebra) --- Algebra --- Noetherian rings. --- Rings, Noetherian --- Associative rings --- Commutative rings --- Anells noetherians
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