# Rings and Ideals

1.a) Let R be a ring with 1 and let S=M2(R). If I is an field of S, show that there is an ideal J of R such that I consists of all 2X2 matrices over J.

1 b) Use the result of 1 a) to prove the following question.

Let R be the ring of 2X2 matrices over reals; suppose that I is an ideal of R.

Show that I =(0) or I=R.

See attached file for full problem description.

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