Degree estimate for subalgebras generated by two elements

  • Leonid Makar-Limanov

    Wayne State University, Detroit, USA
  • Jie-Tai Yu

    University of Hong Kong, China

Abstract

We develop a new combinatorial method to deal with a degree estimate for subalgebras generated by two elements in different environments. We obtain a lower bound for the degree of the elements in two-generated subalgebras of a free associative algebra over a field of zero characteristic. We also reproduce a somewhat refined degree estimate of Shestakov and Umirbaev for the polynomial algebra, that plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong Nagata conjecture.

Cite this article

Leonid Makar-Limanov, Jie-Tai Yu, Degree estimate for subalgebras generated by two elements. J. Eur. Math. Soc. 10 (2008), no. 2, pp. 533–541

DOI 10.4171/JEMS/121