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Abstract algebra

permaneceerc

2021-06-18

If a, b are elements of a ring and m, $n\in Z$, show that $(na)(mb)=(mn)(ab)$

unett

Skilled2021-06-19Added 119 answers

We have to show that if a, $b\in R$ and $m,n\in Z$, then $(na)(mb)=(nm)(ab).$ Notice that

$(na)(mb)=(a+....+a)(b+....+b)n\times m\times =a(b+...+b)+...+a(b+...+b)ms=$

$(ab+...+ab)+...+(ab+...+ab)m\times n\times =m(ab)+...+m(ab)n\times =(nm)(ab)$

Hence the proof.

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