The skew field of fractions of the weyl algebra contains a free noncommutative subalgebra. Makar-Limanov, L. Communications in Algebra, 11(17):2003–2006, January, 1983.
The skew field of fractions of the weyl algebra contains a free noncommutative subalgebra [link]Paper  doi  bibtex   
@article{makar-limanov_skew_1983,
	title = {The skew field of fractions of the weyl algebra contains a free noncommutative subalgebra},
	volume = {11},
	issn = {0092-7872, 1532-4125},
	url = {http://www.tandfonline.com/doi/abs/10.1080/00927878308822945},
	doi = {10.1080/00927878308822945},
	language = {en},
	number = {17},
	urldate = {2016-07-16},
	journal = {Communications in Algebra},
	author = {Makar-Limanov, L.},
	month = jan,
	year = {1983},
	pages = {2003--2006},
}

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