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Show that a ring is commutative if it has the property

Chapter 12, Problem 8E

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QUESTION:

Problem 8E

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

Questions & Answers

QUESTION:

Problem 8E

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

ANSWER:

Step 1 of 2

Let R be a ring with the property that  implies  when

The objective is to prove that R is commutative.

That is to prove that  for all

Let

Assume that

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