AUT Journal of Mathematics and Computing

AUT Journal of Mathematics and Computing

A note on algebraic commutators in division rings with uncountable center

Document Type : Original Article

Author
Vo Hoang Minh Thu 1, 2
1 Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam
2 Vietnam National University, Ho Chi Minh City, Vietnam
10.22060/ajmc.2025.23898.1324
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 \cite[Problems 1 and 5]{Pa_ChFoLe} for division rings with uncountable center.
Keywords
Algebraic element
Uncountable center
Division ring
Left algebraic
Right algebraic
Subjects
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AUT Journal of Mathematics and Computing
Volume 7, Issue 4
Autumn 2026
Pages 441-445