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 HomD(V,V) such that Im θ is finite dimensional, then F is a proper ideal of HomD(V,V). Therefore HomD(V,V) is not simple.
(b) F is itself a simple ring.
(c) F is contained in every nonzero ideal of HomD(V,V).
(d) HomD(V,V) is not (left) Artinian.
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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
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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