Show that a finite ring R with unity 1 ≠ 0 and no divisors of 0 is a division ring. (It is actually a field, although commulalivity is not easy to prove. See Theorem 24.10.) [Note: In your proof, to show that a ≠ 0 is a unit, you must show that a "left multiplicative inverse" of a ≠ 0 in R is also a "right multiplicative inverse."]
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