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Technical Report 17


Let Zm denote the ring of integers modulo m and let [see pdf for notation] denote the complete ring of all [see pdf for notation] matrices over Zm under the usual matrix addition and multiplication. The primary purposes of this paper are to characterize and count all subfields of the ring [see pdf for notation] . Related results are given on field extensions in [see pdf for notation] of subfields of [see pdf for notation] . Partial results on subfields of [see pdf for notation] when R is an arbitrary finite commutative ring with identity are also given. Having basic significance, a partial characterization of rings containing division rings is obtained.


Mathematics | Physical Sciences and Mathematics

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