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Explain why a finite ring must have a nonzero

Chapter 13, Problem 55E

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QUESTION:

Problem 55E

Explain why a finite ring must have a nonzero characteristic.

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QUESTION:

Problem 55E

Explain why a finite ring must have a nonzero characteristic.

ANSWER:

Step 1 of 2

Let R be a ring with m elements that is finite. Then, it is known that the characteristic of R divides m.

Now, if a given ring R is finite, it contains a finite number of elements, then based on the fact stated above, the characteristic of R divides the number of elements of R.

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