Generalized algebraic rational identities of subnormal subgroups in division rings

2015/10/29 by Bui Xuan Hai, Hai, Bui Xuan, Mai Hoang Bien +3
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1510.08720

openalex publication_date 2015/10/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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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