Free Group Algebras in Certain Division Rings

Triangulaizability of Algebras Over Division Rings

A Note on Isomorphic Commutative Group Algebras over Certain Rings

Suppose G is an abelian group and R is a commutative ring with 1 of char(R) = 0. It is proved that if G is R-favorable torsion and RH and RG are R-isomorphic group algebras for some group H , then H is Rfavorable torsion abelian if and only if either inv(R) = ∅ or inv(R) = ∅ and R is an ND-ring. This strengthens results due to W. Ullery (Comm. Algebra, 1986), (Rocky Mtn. J. Math., 1992) and (Co...

triangulaizability of algebras over division rings

Some Results Relevant to Embeddability of Rings (especially Group Algebras) in Division Rings

P. M. Cohn showed in 1971 that given a ring R, to describe, up to isomorphism, a division ring D generated by a homomorphic image of R is equivalent to specifying the set of square matrices over R which map to singular matrices over D, and he determined the conditions that such a set of matrices must satisfy. The present author later developed another version of this data, in terms of closure o...

Explicit Free Groups in Division Rings

Let D be a division ring of characteristic 6= 2 and suppose that the multiplicative group D• = D \ {0} has a subgroup G isomorphic to the Heisenberg group. Then we use the generators of G to construct an explicit noncyclic free subgroup of D•. The main difficulty occurs here when D has characteristic 0 and the commutators in G are algebraic over Q.