# Degree estimate for subalgebras generated by two elements

Leonid Makar-Limanov; Jie-Tai Yu

Journal of the European Mathematical Society (2008)

- Volume: 010, Issue: 2, page 533-541
- ISSN: 1435-9855

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topMakar-Limanov, Leonid, and Yu, Jie-Tai. "Degree estimate for subalgebras generated by two elements." Journal of the European Mathematical Society 010.2 (2008): 533-541. <http://eudml.org/doc/277201>.

@article{Makar2008,

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, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong Nagata conjecture.},

author = {Makar-Limanov, Leonid, Yu, Jie-Tai},

journal = {Journal of the European Mathematical Society},

keywords = {degree estimate; two-generated subalgebras; polynomial algebras; free associative algebras; commmutators; Jacobians; lemma on radicals; degree estimates; two-generator subalgebras; commutators; Jacobians; tame automorphism},

language = {eng},

number = {2},

pages = {533-541},

publisher = {European Mathematical Society Publishing House},

title = {Degree estimate for subalgebras generated by two elements},

url = {http://eudml.org/doc/277201},

volume = {010},

year = {2008},

}

TY - JOUR

AU - Makar-Limanov, Leonid

AU - Yu, Jie-Tai

TI - Degree estimate for subalgebras generated by two elements

JO - Journal of the European Mathematical Society

PY - 2008

PB - European Mathematical Society Publishing House

VL - 010

IS - 2

SP - 533

EP - 541

AB - 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, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong Nagata conjecture.

LA - eng

KW - degree estimate; two-generated subalgebras; polynomial algebras; free associative algebras; commmutators; Jacobians; lemma on radicals; degree estimates; two-generator subalgebras; commutators; Jacobians; tame automorphism

UR - http://eudml.org/doc/277201

ER -

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