Let S be the ring of all n X n matrices over a division ring D. (a)

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Let S be the ring of all n X n matrices over a division ring D.

(a) S has no proper ideals (that is, 0 is a maximal ideal). 8 or argue directly, using the matrices E_r,_s mentioned there.]

(b) S has zero divisors. Consequently,

(i) S ≅ S/0 is not a division ring and

(ii) 0 is a prime ideal which does not satisfy condition (1).

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 15, 2023 03:05 AM

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Let S be the ring of all n X n matrices over a division ring D. (a)

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a Let I be a nonzero ideal of S Then there exists a nonzero matrix A aij I Without loss of ge...View the full answer

Algebra Graduate Texts In Mathematics 73

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