Questions tagged [division-rings]

A division ring is a possibly noncommutative ring where every nonzero element has a two-sided multiplicative inverse.

27 questions
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Infinite dimensional finitely generated algebraic division algebra

Is there a division algebra $D$ with center $K$ that satisfies the following 3 conditions? 1) $D$ is of infinite dimension over $K$; 2) every element of $D$ is algebraic over $K$; 3) $D$ is ...
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Do twisted group rings of free abelian groups admit universal fields of fractions?

Let $R$ be an associative ring with unit. Recall that an epic $R$-field is a ring epimorphism $\alpha\colon R\to D$ to a skew field/division ring $D$. An epic $R$-field $\alpha$ is called a field of ...
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Counterexample for the Skolem-Noether Theorem

If a division ring is finite-dimensional over its center then we can apply Skolem-Noether theorem (which asserts that every endomorphism is a conjugation). Can someone give a counterexample of the ...
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