On the idempotents,nilpotents, units and zero-divisors of finite rings |
| |
Authors: | Hassan Cheraghpour |
| |
Institution: | Department of Mathematics, University of Kurdistan, Sanandaj, Iran. |
| |
Abstract: | In this article, first we find the number of idempotents 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. Moreover, we find an upper bound for the number of idempotents of a finite ring which is in general smaller than the upper bound found by MacHale Proc. R. Ir. 1982;82A(1):9–12]. Finally, we find the above-mentioned numbers in some matrix rings and quaternion rings. |
| |
Keywords: | Idempotent nilpotent unit zero-divisor matrix ring quaternion ring |
|
|