59
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Differential algebraic dependence and Novikov dependence

&
Pages 1061-1071 | Received 27 Feb 2019, Accepted 17 Apr 2019, Published online: 19 Jul 2019

References

  • Shannon D, Sweedler M. Using Gröbner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence. J Symbolic Comput. 1988;6:267–273. doi: 10.1016/S0747-7171(88)80047-6
  • Cox D, Little J, O'Shea D. Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra. 4th ed. Cham: Springer; 2015. (Undergraduate texts in mathematics).
  • Magnus W, Karrass A, Solitar D. Combinatorial group theory: presentations of groups in terms of generators and relations. Reprint of the 1976 second ed. Mineola (NY): Dover Publications, Inc.; 2004.
  • Shirshov AI. Subalgebras of free Lie algebras. (Russian) Mat Sbornik NS. 1953;33(75):441–452.
  • Witt E. Die Unterringe der freien Lieschen Ringe. Math Z. 1956;64:195–216. doi: 10.1007/BF01166568
  • Umirbaev U. Some algorithmic questions concerning associative algebras. Algebra Logic. 1993;32:244–255. doi: 10.1007/BF02261749
  • Kolchin E. Differential algebra and algebraic groups. New York-London: Academic Press; 1973. (Pure and applied mathematics; vol. 54).
  • Ritt J. Differential algebra. New York: Dover Publications, Inc.; 1966.
  • Noskov G. The cancellation problem for a ring of polynomials. (Russian) Sibirsk Mat Zh. 1978;19:1413–1414.
  • Umirbaev U. Algorithmic problems for differential polynomial algebras. J Algebra. 2016;455:77–92. doi: 10.1016/j.jalgebra.2016.02.010
  • Kondratieva MV, Zobnin AI. The membership problem for differential ideals generated by a composition of polynomials. Program Comput Softw. 2006;32:123–127. doi: 10.1134/S0361768806030017
  • Shestakov I, Umirbaev U. Poisson brackets and two generated subalgebras of rings of polynomials. J Amer Math Soc. 2004;17:181–196. doi: 10.1090/S0894-0347-03-00438-7
  • Umirbaev U. Universal enveloping algebras and universal derivations of Poisson algebras. J Algebra. 2012;354:77–94. doi: 10.1016/j.jalgebra.2012.01.003
  • Gel'fand IM, Dorfman IYa. Hamiltonian operators and algebraic structures related to them. Funct Anal Appl. 1979;13:248–262. doi: 10.1007/BF01078363
  • Dzhumadil'daev AS, Lofwall C. Trees, free right-simmetric algebras, free Novikov algebras and identities. Homology Homotopy Appl. 2002;4:165–190. doi: 10.4310/HHA.2002.v4.n2.a8
  • van den Essen A. Polynomial automorphisms and the Jacobian conjecture. Basel: Birkhauser verlag; 2000. (Progress in mathematics; vol. 190).
  • Cohn PM. Free ideal rings and localization in general rings. Cambridge: Cambridge University Press; 2006. (New mathematical monographs; vol. 3).
  • Makar-Limanov L, Shestakov I. Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields. J Algebra. 2012;349:372–379. doi: 10.1016/j.jalgebra.2011.08.008
  • Makar-Limanov L, Umirbaev U. Free Poisson fields and their automorphisms. J Algebra Appl. 2016;15:1650196, (13 pages). doi: 10.1142/S0219498816501966
  • Kondratieva MV, Levin AB, Mikhalev AV, et al. Differential and difference dimension polynomials. Dordrecht: Kluwer Academic Publishers; 1999. (Mathematics and its applications; vol. 461).
  • Duisengaliyeva B, Naurazbekova A, Umirbaev U. Tame and wild automorphisms of differential polynomial algebras in two variables. Fundam Prikl Mat. (Accepted).
  • Goodearl KR, Warfield RB Jr. An introduction to noncommutative Noetherian rings. 2nd ed. Cambridge: Cambridge University Press; 2004. (London mathematical society student texts; vol. 61).
  • Duisengaliyeva B, Umirbaev U. A wild automorphism of a free Novikov algebra. Sib Electron Math Rep. 2018;15:1671–1679.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.