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Pic\((R)\) and the \(R\)-flatness of \(R[X]/I\). (English) Zbl 0442.13009


MSC:

13D15 Grothendieck groups, \(K\)-theory and commutative rings
14C22 Picard groups
13A15 Ideals and multiplicative ideal theory in commutative rings
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13F10 Principal ideal rings

Citations:

Zbl 0256.13008
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Full Text: DOI

References:

[1] Arezzo, M.; Greco, S., Sul gruppo del classi di ideali, Ann. Scuola Norm. Sup. Pisa, 459-483 (1964), Cl. di Sc. XXI, Fase IV · Zbl 0194.06803
[2] Bass, H., Torsion free and projective modules, Trans. Amer. Math. Soc., 102, 319-327 (1962) · Zbl 0103.02304
[3] Bass, H., Algebraic \(K\)-Theory (1968), Benjamin: Benjamin New York · Zbl 0174.30302
[4] E.D. Davis and A.V. Geramita, Efficient generation of maximal ideals in polynomial rings (more on Theorems 4 and 4′), preprint.; E.D. Davis and A.V. Geramita, Efficient generation of maximal ideals in polynomial rings (more on Theorems 4 and 4′), preprint. · Zbl 0365.13008
[5] Fossum, R. M., The Divisor Class Group of a Krull Domain, Ergebnisse der Mathematik, Band 74 (1973), Springer-Verlag: Springer-Verlag New York · Zbl 0256.13001
[6] McAdam, S.; Rush, D. E., Schreier rings, Bull. London Math. Soc., 10, 77-80 (1977) · Zbl 0378.13003
[7] Ohm, J.; Rush, D. E., The finiteness of \(I\) when \(R[X]/I\) is flat, Trans. Amer. Math. Soc., 171, 377-408 (1972) · Zbl 0256.13008
[8] Querré, J., Sur le groupe des classes de diviseurs, C.R. Acad. Sci., t. 284, 397-399 (1977), Paris · Zbl 0364.13008
[9] Sally, J. D.; Vasconcelos, W. V., Flat ideals \(I\), Comm. in Algebra, 3, 531-543 (1975) · Zbl 0315.13010
[10] Samuel, P., Sur les anneaux factoriels, Bull. Soc. Math. France, 89, 155-173 (1961) · Zbl 0101.27305
[11] Traverso, C., Seminormality and Picard group, Ann. della Scuola Norm. Sup. Pisa, 24, 3, 585-595 (1970) · Zbl 0205.50501
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