Coherence of polynomial rings
HTML articles powered by AMS MathViewer
- by B. V. Greenberg and W. V. Vasconcelos
- Proc. Amer. Math. Soc. 54 (1976), 59-64
- DOI: https://doi.org/10.1090/S0002-9939-1976-0417164-2
- PDF | Request permission
Abstract:
The main result is that $A[X]$, the polynomial ring in any number of indeterminates over a coherent ring $A$ of global dimension two, is coherent.References
- José Bertin, Anneaux cohérents réguliers, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A1–A2 (French). MR 279094 N. Bourbaki, Éléments de mathématique. Fasc. XXVII. Algèbre commutative. Chap. 1: Modules plats. Chap. 2: Localisation, Actualités Sci. Indust., no. 1290, Hermann, Paris, 1961. MR36 # 146.
- Brian Greenberg, Global dimension of cartesian squares, J. Algebra 32 (1974), 31–43. MR 364233, DOI 10.1016/0021-8693(74)90169-0
- A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. I, Inst. Hautes Études Sci. Publ. Math. 20 (1964), 259 (French). MR 173675
- Michel Raynaud and Laurent Gruson, Critères de platitude et de projectivité. Techniques de “platification” d’un module, Invent. Math. 13 (1971), 1–89 (French). MR 308104, DOI 10.1007/BF01390094
- Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. MR 0254021
- B. L. Osofsky, Global dimension of valuation rings, Trans. Amer. Math. Soc. 127 (1967), 136–149. MR 206074, DOI 10.1090/S0002-9947-1967-0206074-0 Y. Quentel, Sur le théorème d’Auslander-Buchsbaum, Colloque d’Algèbre Commutative, Univ. de Rennes, 1972.
- Gabriel Sabbagh, Coherence of polynomial rings and bounds in polynomial ideals, J. Algebra 31 (1974), 499–507. MR 347796, DOI 10.1016/0021-8693(74)90128-8
- Hu Sheng, Finiteness in prime ideals in rings of global dimension two, Proc. Amer. Math. Soc. 41 (1973), 363–369. MR 327739, DOI 10.1090/S0002-9939-1973-0327739-4
- Jean-Pierre Soublin, Anneaux et modules cohérents, J. Algebra 15 (1970), 455–472 (French). MR 260799, DOI 10.1016/0021-8693(70)90050-5
- Wolmer V. Vasconcelos, The local rings of global dimension two, Proc. Amer. Math. Soc. 35 (1972), 381–386. MR 308115, DOI 10.1090/S0002-9939-1972-0308115-6
- Wolmer V. Vasconcelos, Rings on global dimension two, Conference on Commutative Algebra (Univ. Kansas, Lawrence, Kan., 1972), Lecture Notes in Math., Vol. 311, Springer, Berlin, 1973, pp. 243–251. MR 0340239
- Wolmer V. Vasconcelos, Coherence of one polynomial ring, Proc. Amer. Math. Soc. 41 (1973), 449–456. MR 325608, DOI 10.1090/S0002-9939-1973-0325608-7
- Wolmer V. Vasconcelos, Conductor, projectivity and injectivity, Pacific J. Math. 46 (1973), 603–608. MR 321919
- Wolmer V. Vasconcelos, Finiteness in projective ideals, J. Algebra 25 (1973), 269–278. MR 314828, DOI 10.1016/0021-8693(73)90045-8
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 59-64
- MSC: Primary 13F20; Secondary 14A05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0417164-2
- MathSciNet review: 0417164