Every subring of a non-commutative ring is non-commutative.This statement is true/false?Please give reasons for your answer ?

1 Answer
George C.
Feb 7, 2018

False

Explanation:

For example, consider the ring of #2xx2# matrices with real coefficients. In general multiplication of such matrices is non-commutative, but the subset of real multiples of the identity matrix form a commutative subring.

Furthermore, any non-commutative ring will contain distinct elements #0# and #1# which generate a commutative subring.

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