On the idempotents, nilpotents, units and zero-divisors of finite rings

In this talk, first we find the number of idempotents, nilpotents and the zero-divisors of a matrix ring over a finite field F.  

Next, given the order of the Jacobson radical of the finite unital ring R, we find the number of units, nilpotents and zero-divisors of R, and give an upper bound for the number of idempotents of R, which is an extension of one of the previously founded results.

Finally, we find the above-mentioned numbers in some matrix rings and quaternion rings.

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