A note on algebraic commutators in division rings with uncountable center

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Document Type : Original Article

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Faculty of Mathematics and Computer Science, University of Sci- ence, Ho Chi Minh City, Vietnam Vietnam National University, Ho Chi Minh City, Vietnam

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∈D∖C. The purpose of this paper is to prove that if either axa−1x−1 or xy−yx is right algebraic over K for all x,y∈D∖{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.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 11 March 2025

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