Cohn, P. M. An embedding theorem for free associative algebras. (English) Zbl 0729.16010 Math. Pannonica 1, No. 1, 49-56 (1990). One of the many manifestations of the striking difference between commutative and noncommutative settings is the possibility of putting “big” objects inside small ones. For example, it is well-known (to the experts) that an algebra F of noncommutative polynomials (a free associative algebra) with a countable number of generators can be imbedded in the algebra G of noncommutative polynomials with two generators. The author gives a construction of such an imbedding of F into G that may be extended to an imbedding of analogs of fields of rational functions. This construction also provides a (relatively) simple example of a so-called 1-inert imbedding, which means that any factorization of \(f\in F\), considered as an element of G, is essentially a factorization in f itself. Reviewer: L.G.Makar-Limanov (Detroit) Cited in 1 Document MSC: 16K40 Infinite-dimensional and general division rings 16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 16S36 Ordinary and skew polynomial rings and semigroup rings Keywords:free associative algebra; generators; noncommutative polynomials; fields of rational functions; 1-inert imbedding; factorization PDFBibTeX XMLCite \textit{P. M. Cohn}, Math. Pannonica 1, No. 1, 49--56 (1990; Zbl 0729.16010) Full Text: EuDML