Let R be a commutative ring and M₂(R) the ring of 2-by-2matrices with entries in R (with the usual matrix addition and multiplication). Prove thatif I is an ideal in R then M2(I) is an ideal in M₂(R).

In the given proof, we showed that if I is an ideal in a commutative ring R, then the set M2(I) of…

Answered: Let R be a commutative ring and M₂(R)…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 31E: Let R be a commutative ring that does not have a unity. For a fixed aR, prove that the set...

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Let R be a commutative ring and M₂(R) the ring of 2-by-2 matrices with entries in R (with the usual matrix addition and multiplication). Prove that if I is an ideal in R then M2(I) is an ideal in M₂(R).