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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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Aug 03, 2023 08:17 AM

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Let R be the ring of 2 2 matrices over an infinite field. (a) R has

Question:

Step by Step Answer:

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

Algebra Graduate Texts In Mathematics 73

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