A note on algebraic commutators in division rings with uncountable center

	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 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
آمار تعداد مشاهده مقاله: 282