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Subrings and Division Rings

Prove that any finite subring of a division ring is a division ring.

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let R be a division ring, and S a finite subring of R with a 1.

observe that a unit of any ring with identity cannot be a zero divisor; to this end, suppose that a is a unit; ...

Solution Summary

Subrings and Division Rings are investigated. The solution is detailed and well presented.