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On two conjectures about polynomial rings. (English) Zbl 0395.13009

MSC:
13E15 Commutative rings and modules of finite generation or presentation; number of generators
13E05 Commutative Noetherian rings and modules
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13C15 Dimension theory, depth, related commutative rings (catenary, etc.)
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References:
[1] Bass, H.: Liberation des Modules Projectifs sur certains anneaux de Polynomes. Seminaire Bourkaki, 26 e annee, 448 (1973/74)
[2] Eisenbud, D., Evans, E.G., Jr.: Three Conjectures about Modules over Polynomial Rings. Conference on Commutative Algebra, Lecture Notes in Math. No. 311. Berlin, Heidelberg, New York: Springer 1973 · Zbl 0265.13004
[3] Eisenbud, D., Evans, E.G., Jr.: Generating Modules efficiently: Theorems from AlgebraicK-Theory. J. Algebra27/2, 278-305 (1973) · Zbl 0286.13012
[4] Forster, O.: Über die Anzahl der Erzeugenden eines Ideals in einem Noetherschen Ring. Math. Z.48, 80-87 (1964) · Zbl 0126.27303
[5] Mohan Kumar, N.: Complete Intersections. (To appear) · Zbl 0384.14016
[6] Murthy, M.P.: Generators for Certain Ideals in Regular Rings of Dimension Three. Comment. Math. Helv.47, 179-184 (1972) · Zbl 0251.13006
[7] Quillen, D.: Projective Modules over Polynomial Rings. Inventiones math.36, 166-172 (1976) · Zbl 0337.13011
[8] Sathaye, A.M.: On the Forster-Eisenbud-Evans Conjecture, Inventiones math.46, 211-224 (1978) · Zbl 0382.13004
[9] Szpiro, L.: Surfaces containing a given imbedded curve. Tata Institute Lecture Notes in Math. (To appear)
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