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On free group algebras in division rings with uncountable center

Jairo Z. Gonçalves, M. Shirvani

Proceedings of the American Mathematical Society · 1996 · 23 citations · 10 references

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Abstract

Let $D$ be a division algebra with uncountable center $k$. If $D$ contains a noncommutative free $k$-algebra, then $D$ also contains the $k$-group algebra of the free group of rank 2.

References

10

The skew field of fractions of the weyl algebra contains a free noncommutative subalgebra

Leonid Makar-Limanov · Communications in Algebra · 1983 · 69 citations

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On subgroups of the multiplicative group of skew fields

A. I. Lichtman · Proceedings of the American Mathematical Society · 1977 · 49 citations · Full text

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On normal subgroups of multiplicative group of skew fields generated by a polycyclic-by-finite group

A. I. Lichtman · Journal of Algebra · 1982 · 34 citations

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On group rings of nilpotent groups

Leonid Makar-Limanov · Israel Journal of Mathematics · 1984 · 32 citations

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Free subalgebras of enveloping fields

Leonid Makar-Limanov, Peter Malcolmson · Proceedings of the American Mathematical Society · 1991 · 26 citations

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