References
- Aschenbrenner, M. (2001). Ideal membership in polynomial rings over the integers. Ph.D. Thesis. University of Illinois at Urbana-Champaign.
- Aschenbrenner, M. (2004). Ideal membership in polynomial rings over the integers. J. Am. Math. Soc. 17:407–441.
- Aschenbrenner, M. (2005). Bounds and definability in polynomial rings. Quart. J. Math. 56:263–300.
- Aschenbrenner, M. An effective Weierstrass division theorem, preprint. https://www.math.ucla.edu/matthias/pdf/ideal4.pdf.
- Bombieri, E., Gubler, W. (September 24, 2007). Heights in Diophantine Geometry, 1st ed. New Mathematical Monographs 4, Cambridge: Cambridge University Press.
- Bourbaki, N. (1972). Commutative Algebra. Paris: Hermann.
- Bourbaki, N. (2003). Elements of Mathematics, Algebra 2, Chapters 4–7. Springer; 1st ed. 1990. 2nd printing 2003 edition.
- Eisenbud, D. (2004). Commutative Algebra with a View toward Algebraic Geometry. Springer New York: Springer-Verlag.
- Goldblatt, R. (1998). Lectures on the Hyperreals, A Introduction to Nonstandard Analysis. New York: Springer-Verlag.
- Göral, H. (2015). Model theory of fields and heights. Ph.D. Thesis. Lyon.
- Henson, C. W. Foundation of Nonstandard Analysis, A Gentle Introduction to Nonstandard Extensions. Lecture Notes. https://pdfs.semanticscholar.org/86fe/d3b5ebc6ad2b593af24a6a196355d3b19be6.pdf
- Hentzelt, K., Noether, E. (1923). Zur theorie der polynomideale und resultanten. Math. Ann. 88:53–79.
- Hermann, G. (1926). Die frage der endlich vielen schritte in der theorie der polynomideale. Math. Ann. 95:736–788.
- Hindry, M., Silverman, J. H. (2000). Diophantine Geometry, An Introduction. New York: Springer-Verlag.
- Kani, E. (1978). Nonstandard diophantische geometrie, insbesondere Satz von Mordell-Weil. Ph.D. Thesis. Universität Heidelberg.
- Kollár, J. (1988). Sharp effective Nullstellensatz. J. Am. Math. Soc. 1(4):963–975.
- Lehmer, D. H. (1933). Factorization of certain cyclotomic functions. Ann. Math. (2) 34:461–479.
- Marker, D. (2002). Model Theory: An Introduction. New York: Springer-Verlag.
- Matsumura, H. (1980). Commutative Algebra, 2nd ed. Benjamin-Cummings Pub Co; Subsequent edition, USA.
- Moriwaki, A. (2000). Arithmetic height functions over finitely generated fields. Arithmetic height functions over finitely generated fields140:101–142.
- Robinson, A. (1955). Théorie Métamathématiques des Idéaux. Collection de Logique Mathématiques, Ser A. Dactyl-offset. Gauthier-Villars, Paris; E. Nauwelaerts, Louvain.
- Robinson, A. (1960). Some problems of definability in the lower predicate calculus. J. Symbolic Logic 25(2):171.
- Schmidt, K. (1989). Polynomial bounds in polynomial rings over fields. J. Algebra 125:164–180.
- Seidenberg, A. (1974). Constructions in algebra. Trans. AMS 197:273–313.
- Smyth, C. (2008). The Mahler Measure of Algebraic Numbers: A Survey. Number Theory and Polynomials. London Math. Soc. Lecture Note Ser., Vol. 352. Cambridge: Cambridge University Press, pp. 322–349.
- Sombra, M. (1999). Sparse effective Nullstellensatz. Adv. Appl. Math. 22(2):271–295.
- van den Dries, L., Schmidt, K. (1984). Bounds in the theory of polynomial rings over fields. A nonstandard approach. Invent. Math. 76:77–91.