Division Rings and Herstein's Conjecture

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Aghayari, Ghasem | 2021

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 53767 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Hezavehi, Mohammad
Abstract:
In algebra, division rings or skew fields are considered one of the basic building blocks in ring theory. So, a careful study of the properties of these rings is essential for the development of ring theory. All division rings, according to whether they are finite dimensional or infinite dimensional (as vector spaces) over their centers, are broadly classified into two types of centrally finite division rings and centrally infinite division rings.Herstein's conjecture about multiplicative commutators in these rings, is one of the unsolved problems that Herstein has proved it in the case when division ring is centrally finite, or the center of division ring is uncountable, but the general case is still open.In this thesis, we will study division rings and Herstein's conjecture in these rings
Keywords:
Division Rings ; Commutators ; Division Algebra ; Herstein's Conjecture