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arXiv · 1510.08720

Generalized algebraic rational identities of subnormal subgroups in division rings

Bui Xuan Hai·Mai Hoang Bien·Truong Huu Dung
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Abstract

In this note, we introduce a new concept of a {\it generalized algebraic rational identity} to investigate the structure of division rings. The main theorem asserts that if a non-central subnormal subgroup $N$ of the multiplicative group $D^*$ of a division ring $D$ with center $F$ satisfies a non-trivial generalized algebraic rational identity of bounded degree, then $D$ is a finite dimensional vector space over $F$. This generalizes some previous results.

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Bui Xuan Hai, Mai Hoang Bien, Truong Huu Dung. 2015-10-29. Generalized algebraic rational identities of subnormal subgroups in division rings. https://arxiv.org/abs/1510.08720

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