Show that a ring is commutative if it has the property that ab = ca implies b = c when a != 0.



Answered question


If a ring has the characteristic that, then prove that it is commutative ab = ca implies b = c when a0.

Answer & Explanation



Skilled2020-10-20Added 95 answers

Since R is ting, therefore by propery of ring we have,
a(ba)=(ab)a for all a,bR
Now, applying given condition on the above property, we get
ba=ab for all a,bR
Therefore, R is cpmmuttive ring
Hene, proved

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Commutative Algebra

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?