## Document Type

Report

## Source Publication Title

Technical Report 17

## Abstract

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.

## Disciplines

Mathematics | Physical Sciences and Mathematics

## Publication Date

10-1-1974

## Language

English

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

## Recommended Citation

McConnel, Robert M. and Beard Jr., Jacob T. B., "Matrix Fields Over the Integers Modulo m" (1974). *Mathematics Technical Papers*. 84.

https://mavmatrix.uta.edu/math_technicalpapers/84