Büchi sequences in local fields and local rings

• Autorzy: Browkin J.
• Języki publikacji: EN

Abstrakty

EN

We prove that there exist infinite Büchi sequences in some local rings and local fields, with the exception of the ring Zp of p-adic integers. In Zp there are only finite but arbitrarily long Büchi sequences.

Słowa kluczowe

EN

Buchi sequence; local rings; local fields

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: Vol. 58, no 2
• Strony: 109--115
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Browkin J.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland,

Bibliografia

• [1] H. Fasten, T. Pheidas and X. Vidaux, A survey on Büchi’s problem: new presentations and open problems, Proc. Hausdorff Institute of Mathematics, to appear.
• [2] W. M. Schmidt, Equations over Finite Fields: An Elementary Approach, 2nd ed., Kendrick Press, 2004.
• [3] P. Vojta, Diagonal quadratic forms and Hilbert’s Tenth Problem, in: Contemp. Math. 270, Amer. Math. Soc., 2000, 261-274.
• [4] E. Weiss, Algebraic Number Theory, McGraw-Hill, 1963.