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Division subring S = division ring D or S is a subset of D

Modern Algebra
Division Ring

Let D be a division ring, Z its center and let S be a division subring of D which is stabilized by every map
x→dxd-1, d ≠ 0 in D. Show that either S = D or S is a subset of D.

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Modern Algebra
Division Ring

Solution Summary

This solution is comprised of a detailed explanation of the problems of division rings. It contains step-by-step explanation for the problem.