Let V be an infinite dimensional vector space over a division ring D. (a) If F is

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Let V be an infinite dimensional vector space over a division ring D.

(a) If F is the set of all θ ϵ Hom_D(V,V) such that Im θ is finite dimensional, then F is a proper ideal of Hom_D(V,V). Therefore Hom_D(V,V) is not simple.

(b) F is itself a simple ring.

(d) Hom_D(V,V) is not (left) Artinian.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Aug 18, 2023 05:52 AM

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Let V be an infinite dimensional vector space over a division ring D. (a) If F is

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a Let HomDVV such that Im is infinite dimensional Then for any nonzero vector v V the map Id ...View the full answer

Algebra Graduate Texts In Mathematics 73

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