A note on algebraic commutators in division rings with uncountable center | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 6، دوره 7، شماره 4، زمستان 2026، صفحه 441-445 اصل مقاله (327.38 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2025.23898.1324 | ||
| نویسنده | ||
| Vo Hoang Minh Thu* 1، 2 | ||
| 1Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam | ||
| 2Vietnam National University, Ho Chi Minh City, Vietnam | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Algebraic element؛ Uncountable center؛ Division ring؛ Left algebraic؛ Right algebraic | ||
| مراجع | ||
|
| ||
|
آمار تعداد مشاهده مقاله: 385 تعداد دریافت فایل اصل مقاله: 51 |
||