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

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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

xâ†’dxd-1, d â‰ 0 in D. Show that either S = D or S is a subset of D.

See the attached file.

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:15 pm ad1c9bdddfhttps://brainmass.com/math/ring-theory/division-subrings-division-ring-subset-37699

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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

xâ†’dxd-1, d â‰ 0 in D. Show that either S = D or S is a subset of D.

See the attached file for the solution of the problem.

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Â© BrainMass Inc. brainmass.com December 24, 2021, 5:15 pm ad1c9bdddf>https://brainmass.com/math/ring-theory/division-subrings-division-ring-subset-37699