By David S. Dummit, Richard M. Foote

"Widely acclaimed algebra textual content. This publication is designed to offer the reader perception into the ability and wonder that accrues from a wealthy interaction among varied components of arithmetic. The e-book conscientiously develops the speculation of other algebraic buildings, starting from uncomplicated definitions to a few in-depth effects, utilizing quite a few examples and routines to help the reader's realizing. during this method, readers achieve an appreciation for a way mathematical buildings and their interaction bring about robust effects and insights in a couple of varied settings."

Covers basically all undergraduate algebra. Searchable DJVU.

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P Sc~ . ( X + v') = X + sc, v ' = ~ + v. v> = 0 und = 54 Damit ist der Satz bewiesen. 10 Seien 0h ~ ~- h~- antidominant mit % - ~- P(R). FOr alle M in g-Moduln setzen wir ii T~M (M @ V(p - %)) U Offensichtlich induziert T~ einen exakten Funktor von diesen Funktor Verschiebung Satz: Seien % nach %, ~ E hm antidominant der Facette yon in ~ ; wir nennen ~. mit ~ - N C P(R). Es liege R~ im Abschlug ~. %) ~ H ( w . % = for alle klar; mit ~' die Voraussetzungen w. A + ~' wir mOssen also beweisen, # w(p - %) + ~' @ = M in E = V(~ -%) , jenes Satzes folgt dann unsere Behauptung.

L ~ i ~ n Fdr alle u ~ U(n__-) gilt offensichtlich u(v 8 e i) ~ (uv) ~ e i + U(n-)v 8 U(n )n e i. Nach Wahl der Nur~nerierung der e. ist U(n )n e. l e. J mit j < i (I) enthalten. -- j

FHr alle ~ 6h ~ fur alle ~S'' U(~) ~ ~ S es gilt B = S ~ S' und ~S = B ~ S' ~S' ist. und ist zum Tensorprodukt k~nnen wit M(A) mit MS(A S ) 0 MS'(AS,) identifizieren. Satz b) a) F~r alle Ffir alle A ~h ~ A, ~ E h ~[(A) : e(~)] und Gewicht a) auf ]MS(Xs) = = LS(%S) und LS(%s) @ LS'(%S,). also isomorph zu L(%). zu LS(As) 0 LS'(AS, ) isomorph. : LS(~s )] ~ S' LM (%S,) : L S' (HS,) j (LS(As) : MS(Ns))(LS'(%S, ) : MS'(HS,)). Offensichtlich ist %S + %S' = % " Formen auf L(%) gilt (L(A) : M(~)) Beweis: ist LS(%s) @ LS'(%S,) ein ~-Modul zum hSchsten Das Tensorprodukt von nicht ausgearteten kontravarianten LS'(%S,) ist eine nicht ausgeartete kontravariante Form Nach Satz I~6 ist LS(%s) @ LS'(%S ,) deshalb einfach, 40 b) Diese Formeln folgen aus (nach a)) eh L(k) = ch LS(ks ) .

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