شماره ركورد كنفرانس :
3502
عنوان مقاله :
Vector Space Generated by the Multiplicative Commutators of a Division Ring
Author/Authors :
S Akbari Sharif University of Technology , A Madadi University of Zanjan , M Ariannejad University of Zanjan , M Aaghabali Shahid Soltani Center for Talented Students, Karaj
كليدواژه :
Multiplicative Commutator , Trace Function , Division Ring
عنوان كنفرانس :
چهل و پنجمين كنفرانس رياضي ايران
چكيده لاتين :
Let D be a division ring with center F. An element of the form xyx(−1)y(−1) ∈ D is called a
multiplicative commutator. Let T(D) be the vector space over F generated by all multiplicative commutators
in D. In this paper it is shown that if D is algebraic over F and Char(D) = 0, then D = T(D). We conjecture
that it is true in general. Among other results it is shown that in characteristic zero if T(D) is algebraic
over F, then D is algebraic over F.
