JournalsjemsVol. 10 , No. 2DOI 10.4171/jems/121

Degree estimate for subalgebras generated by two elements

  • Leonid Makar-Limanov

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

    University of Hong Kong, China
Degree estimate for subalgebras generated by two elements cover

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.