We classify the maximal subrings of the ring of nx n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.
Maximal Subrings and Covering Numbers of Finite Semisimple Rings
Peruginelli, G.
;Werner, N. J.
2018
Abstract
We classify the maximal subrings of the ring of nx n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.
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