Advances in Non-Commutative Ring Theory: Proceedings of the by Patrick J. Fleury (auth.) PDF

By Patrick J. Fleury (auth.)

ISBN-10: 3540115978

ISBN-13: 9783540115977

ISBN-10: 3540393714

ISBN-13: 9783540393719

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Dieses Buch ist eine moderne Einführung in die Algebra, kompakt geschrieben und mit einem systematischen Aufbau. Der textual content kann für eine ein- bis zweisemestrige Vorlesung benutzt werden und deckt alle Themen ab, die für eine breite Algebra Ausbildung notwendig sind (Gruppentheorie, Ringtheorie, Körpertheorie) mit den klassischen Fragen (Quadratur des Kreises, Auflösung durch Radikale, Konstruktionen mit Zirkel und Lineal) bis zur Darstellungstheorie von endlichen Gruppen und einer Einführung in Algebren und Moduln.

Additional info for Advances in Non-Commutative Ring Theory: Proceedings of the Twelfth George H. Hudson Symposium Held at Plattsburgh, USA, April 23–25, 1981

Example text

N By [5, Proposition is right T-nilpotent. 7], conditions Conditions (ii) and (iii) imply that (i) and (ii) imply that R has finite reduced rank, by Theorem i. D Goldman has shown R is left Artinian next theorem extends Let THEOREM (3). 10]. T-nilpotent. ,S n of simple modules, the zero functor. THEOREM (4). Let then torsion radical. and so and RR for of the equivalence S be ~ r i t a equivalent rings. Let F: classes R-Mod, which implies that has finite length. ~ is R If R has finite reduced S.

Corollary 2: If R is a stable FBN ring with P a prime ideal then Rp is a stable FBN ring. Proof: Muller [24, Thm. ii] has shown that for stable FBN rings, the left localization of R at P coincides with the right localization of R at P. The result now follows from proposition i. o It is of interest to remark that if right noetherian is 50 omitted from the hypotheses localizable at every prime Example: commutative S-module, of proposition ideal. Let S = F[[x]], field F. i, R may not be left the power Let M = F[[x]] series ring over a viewed naturally but as a right F[[x]]-module as a left via the quotient ring epimorphism F[[x]] -~ F -+ o .

Thus, of this 9enerated left remark to be finitely in mod-R, that to prove Bass' The proof generated then inasmuch 2. 1, O is left Noetherian. This from T h e o r e m M* implies is finitely as stated, result referred shows right R - m o d u l e M c--~Rn generated. ) to earlier. that the dual m o d u l e M embeds M* in a finitely free module. ACKNOWLEDGEMENT This paper was discussed impromptu during the problem session. 5C. M. , Torsion integral-domains, [66] Osofsky, Faith, 4 (1966) modules, modules 15 (1963) over non- 132-151.

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Advances in Non-Commutative Ring Theory: Proceedings of the Twelfth George H. Hudson Symposium Held at Plattsburgh, USA, April 23–25, 1981 by Patrick J. Fleury (auth.)


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