Let R be a ring with unity 1. If 1 has infinite order under addition then the characteristic of R is 0. If 1 has order n under addition , then the characteristic of R is n.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 22E: 22. Let be a ring with finite number of elements. Show that the characteristic of divides .
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Let R be a ring with unity 1. If 1 has infinite order under addition then the characteristic of R is 0. If 1 has order n under addition , then the characteristic of R is n.
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