Let R be a field of real numbers and M₂(R) be a ring of 2 x 2 matrices over R under usual operations, then: a) If S is a subring of M,(R). then S is an ideal of M₂(R). b) If S is an ideal of M₂(R), the S is a subring of M₂(R). c) There are no two non-trivial subrings S, and S2 of M₂(R) such that S, US, is a subring of R. dy For any two ideals I, and 12 of M₂(R). then I, U 12 is not ideal of M₂(R)

Let R be a field of real numbers and M₂(R) be a ring of 2 x 2 matrices over R under usual operations, then: a) If S is a subring of M,(R). then S is an ideal of M₂(R). b) If S is an ideal of M₂(R), the S is a subring of M₂(R). c) There are no two non-trivial subrings S, and S2 of M₂(R) such that S, US, is a subring of R. dy For any two ideals I, and 12 of M₂(R). then I, U 12 is not ideal of M₂(R)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 11E: Let R be the set of all matrices of the form [abba], where a and b are real numbers. Assume that R...

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