In class we defined the characteristic of a field the defini

In class, we defined the characteristic of a field; the definition of the characteristic of a ring with unity is the same. That is, the characteristic of a ring with unity R is the smallest positive integer k such that 1 + 1 + · · · + 1= 0?k copies of 1 . If no such k exists, the characteristic is zero. Let m, n be positive integers. Find the characteristic of Zm ? Zn.

Problem 4: In class, we defined the characteristic of a field; the definition of the characteristic of a ring with unity is the same. That is, the characteristic of a ring with unity R is the smallest positive integer k such that k copies of 1 If no such k exists, the characteristic is zero. Let m, n be positive integers. Find the characteristic of Zn® Zn.

Solution