Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 7 4 2026 10 01 A note on algebraic commutators in division rings with uncountable center 441 445 5698 10.22060/ajmc.2025.23898.1324 EN Vo Hoang Minh Thu Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam Vietnam National University, Ho Chi Minh City, Vietnam Journal Article 2025 02 13 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. https://ajmc.aut.ac.ir/article_5698_7f848746fe2599dc199a75f0d02fc3d6.pdf