Let R be the ring of 2 2 matrices over an infinite field. (a) R has
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Let R be the ring of 2 × 2 matrices over an infinite field.
(a) R has an infinite number of distinct proper left ideals, any two of which are isomorphic as left R-modules.
(b) There are infinitely many distinct pairs (B, C) such that Band Care minimal left ideals of R and R = B ⊕ C.
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To prove the statements in question well proceed step by step a R has an infinite number of distinct proper left ideals any two of which are isomorphic as left Rmodules First lets recall what an ideal ...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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