Publication: A Review of the theory of completely primary finite rings
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Abstract
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.
Description
Paper presented at Strathmore International Math Research Conference on July 23 - 27, 2012
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.
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.
Keywords
Finite rings, Completely primary, Galois subrings, Cyclic modules, Classification (MSC2010), Primary 16P10, Secondary 20K01.1