14,123 research outputs found
On subgroups in division rings of type
Let be a division ring with center . We say that is a {\em
division ring of type } if for every two elements the division
subring is a finite dimensional vector space over . In this paper
we investigate multiplicative subgroups in such a ring.Comment: 10 pages, 0 figure
Certain Simple Maximal Subfields in Division Rings
Let D be a division ring finite dimensional over its center F. The goal of
this paper is to prove that for any positive integer n there exists a in D^(n);
the n-th multiplicative derived subgroup, such that F(a) is a maximal subfield
of D. We also show that a single depth-n iterated additive commutator would
generate a maximal subfield of D.Comment: We have made some editorial changes as well as changes in Lemma 9 and
Theorem 1
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