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Explain why a finite ring must have a nonzero
Chapter 13, Problem 55E(choose chapter or problem)
QUESTION:
Problem 55E
Explain why a finite ring must have a nonzero characteristic.
Questions & Answers
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.