A note on algebraic commutators in division rings with uncountable center

Articles in Press

Document Type : Original Article

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Faculty of Mathematics and Computer Science, University of Sci- ence, Ho Chi Minh City, Vietnam Vietnam National University, Ho Chi Minh City, Vietnam

Abstract

Let $D$ be a division ring with uncountable center $C$. Suppose that \( K \) is a sub-division ring of \( D \) containing $C$ and that \( a \in D \setminus C \). The purpose of this paper is to prove that if either \( axa^{-1}x^{-1} \) or \( xy - yx \) is right algebraic over \( K \) for all \( x, y \in D \setminus \{0\} \), then \( D \) is also right algebraic over \( K \). This result provides the affirmative answers to [8, Problems 1 and 5] for division rings with uncountable center.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 11 March 2025

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