Strongly \'etale difference algebras and Babbitt's decomposition

Preprint English OPEN
Tomašić, Ivan; Wibmer, Michael;
(2015)
  • Subject: Mathematics - Commutative Algebra | Mathematics - Algebraic Geometry | 12H10

We introduce a class of strongly \'{e}tale difference algebras, whose role in the study of difference equations is analogous to the role of \'{e}tale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's decomposition theorem and we pr... View more
  • References (18)
    18 references, page 1 of 2

    [Bab62] Albert E. Babbitt, Jr. Finitely generated pathological extensions of difference fields. Trans. Amer. Math. Soc., 102:63-81, 1962.

    [Bou72] Nicolas Bourbaki. Elements of mathematics. Commutative algebra. Hermann, Paris, 1972. Translated from the French.

    [Bou90] N. Bourbaki. Algebra. II. Chapters 4-7. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 1990. Translated from the French by P. M. Cohn and J. Howie.

    [CHP02] Zo´e Chatzidakis, Ehud Hrushovski, and Ya'acov Peterzil. Model theory of difference fields. II. Periodic ideals and the trichotomy in all characteristics. Proc. London Math. Soc. (3), 85(2):257-311, 2002.

    [Coh65] Richard M. Cohn. Difference algebra. Interscience Publishers John Wiley & Sons, New York-LondonSydeny, 1965.

    [DVHW14] Lucia Di Vizio, Charlotte Hardouin, and Michael Wibmer. Difference Galois theory of linear differential equations. Adv. Math., 260:1-58, 2014.

    [Hru04] Ehud Hrushovski. The elementary theory of the Frobenius automorphisms, 2004. arXiv:math/0406514v1, updated version available from http://www.ma.huji.ac.il/∼ ehud/.

    [Lev08] Alexander Levin. Difference algebra, volume 8 of Algebra and Applications. Springer, New York, 2008.

    [Mil12] James S. Milne. Basic theory of affine group schemes, 2012. Available at www.jmilne.org/math/.

    [Spr09] T. A. Springer. Linear algebraic groups. Modern Birkh¨auser Classics. Birkh¨auser Boston, Inc., Boston, MA, second edition, 2009.

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