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A note on algebraic commutators in division rings with uncountable center | ||
| AUT Journal of Mathematics and Computing | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 اسفند 1403 | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2025.23898.1324 | ||
| نویسنده | ||
| Vo Hoang Minh Thu* | ||
| Faculty of Mathematics and Computer Science, University of Sci- ence, Ho Chi Minh City, Vietnam Vietnam 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 [8, Problems 1 and 5] for division rings with uncountable center. | ||
| کلیدواژهها | ||
| algebraic element؛ uncountable center؛ division ring؛ left algebraic؛ right algebraic | ||
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آمار تعداد مشاهده مقاله: 245 |
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