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Ultraproducts and approximation in local rings. II. (English) Zbl 0426.13010


MSC:

13J10 Complete rings, completion
13L05 Applications of logic to commutative algebra
12L10 Ultraproducts and field theory
14B12 Local deformation theory, Artin approximation, etc.
13H99 Local rings and semilocal rings
13E05 Commutative Noetherian rings and modules

Citations:

Zbl 0416.13004
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References:

[1] Artin, M.: On the solution of analytic equations. Invent. Math.5, 277-291 (1968) · Zbl 0172.05301
[2] Artin, M.: Algebraic approximation of structures over complete local rings. Publ. Math. I.H.E.S.36, 23-56 (1969) · Zbl 0181.48802
[3] Becker, J., Denef, J., Lipshitz, L., van den Dries, L.: Ultraproducts and approximation in local rings. I. Invent. Math.51, 189-203 (1979) · Zbl 0416.13004
[4] Gabriélov, A.M.: Formal relations between analytic functions. Funkcional. Anal. i. Prilo?en.5, 64-65 (1971); Functional Anal. Appl.5, 318-319 (1971)
[5] Kurke, H., Pfister, G., Popescu, D., Roczen, M., Mostowski, T.: Die Approximationseigenschaft lokaler Ringe. Lecture Notes in Mathematics, No. 634. Berlin, Heidelberg, New York: Springer 1978 [Zbl.401, 13013 (1979)] · Zbl 0401.13013
[6] Lang, S.: Algebra. Reading, MA: Addison-Wesley 1965
[7] Pfister, G.: Einige Bemerkungen zur Struktur lokaler Henselscher Ringe. Beiträge Algebra Geometrie4, 47-51 (1975) · Zbl 0322.13014
[8] Pfister, G., Popescu, D.: Die strenge Approximationseigenschaft lokaler Ringe. Invent. Math.30, 145-174 (1975) · Zbl 0308.13026
[9] Siu, Yum-Tong: Noetherianness of rings of holomorphic functions on Stein compact subsets. Proc. Am. Math. Soc.21, 483-489 (1969) · Zbl 0175.37402
[10] Tate, J.: Rigid analytic spaces. Invent. Math.12, 257-289 (1971) · Zbl 0212.25601
[11] Van der Put, M.: A Problem on coefficient fields and equations over local rings. Compositio Math.30, 235-258 (1975) · Zbl 0304.13018
[12] Wavrik, J.J.: A theorem on solutions of analytic equations with applications to deformations of complex structures. Math. Ann.216, 127-142 (1975) · Zbl 0303.32018
[13] Zariski, O., Samuel, P.: Commutative algebra. I, II. Princeton: Van Nostrand 1960 · Zbl 0121.27801
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