A Review of the theory of completely primary finite rings

Paper presented at Strathmore International Math Research Conference on July 23 - 27, 2012We give a review of recent developments in the theory of finite rings with identity and pay special attention to a class of finite rings whose sets of all zero divisors form additive groups. We further describe the structure of such rings and provide a general representation for these rings as additive direct sums of cyclic modules over their maximal Galois subrings.We give a review of recent developments in the theory of finite rings with identity and pay special attention to a class of finite rings whose sets of all zero divisors form additive groups. We further describe the structure of such rings and provide a general representation for these rings as additive direct sums of cyclic modules over their maximal Galois subrings