Sur les algèbres universelles
Annales de l'Institut Fourier, Tome 14 (1964) no. 2, pp. 33-87.

Tout d’abord on tâche de comparer les algèbres symétriques et de Rees d’un idéal. Comme conséquence, ceci nous donne une nouvelle caractérisation des anneaux locaux réguliers. L’intégrité de l’algèbre symétrique y joue un rôle essentiel. Dans la deuxième partie, le problème d’injectivité pour les algèbres universelles est envisagé, bien qu’il ne soit étudié ici que pour l’algèbre symétrique. Ensuite, on étend la notion d’anneau de Rees d’un idéal au cas d’un module ; cette algèbre de Rees se localise d’une façon naturelle. La dernière partie est consacrée à l’étude de la projectivité des algèbres universelles d’un module projectif et à l’étude de certaines questions de factorialité liées aux algèbres symétriques.

@article{AIF_1964__14_2_33_0,
     author = {Micali, Artibano},
     title = {Sur les alg\`ebres universelles},
     journal = {Annales de l'Institut Fourier},
     pages = {33--87},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {14},
     number = {2},
     year = {1964},
     doi = {10.5802/aif.173},
     mrnumber = {31 #1275},
     zbl = {0152.02602},
     language = {fr},
     url = {https://www.numdam.org/articles/10.5802/aif.173/}
}
TY  - JOUR
AU  - Micali, Artibano
TI  - Sur les algèbres universelles
JO  - Annales de l'Institut Fourier
PY  - 1964
SP  - 33
EP  - 87
VL  - 14
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - https://www.numdam.org/articles/10.5802/aif.173/
DO  - 10.5802/aif.173
LA  - fr
ID  - AIF_1964__14_2_33_0
ER  - 
%0 Journal Article
%A Micali, Artibano
%T Sur les algèbres universelles
%J Annales de l'Institut Fourier
%D 1964
%P 33-87
%V 14
%N 2
%I Institut Fourier
%C Grenoble
%U https://www.numdam.org/articles/10.5802/aif.173/
%R 10.5802/aif.173
%G fr
%F AIF_1964__14_2_33_0
Micali, Artibano. Sur les algèbres universelles. Annales de l'Institut Fourier, Tome 14 (1964) no. 2, pp. 33-87. doi : 10.5802/aif.173. https://www.numdam.org/articles/10.5802/aif.173/

[1] N. Bourbaki, Algèbre, chap. II (Algèbre Linéaire), 3e édition, Hermann, Paris, 1962.

[2] N. Bourbaki, Algèbre, Chap. III (Algèbre Multilinéaire), 2e édition, Hermann, Paris, 1958.

[3] N. Bourbaki, Algèbre Commutative, chap. I et II, Hermann, Paris, 1961.

[4] N. Bourbaki, Algèbre Commutative, chap. VI, à paraître.

[5] P. Cartier, Questions de rationnalité des diviseurs en Géométrie Algébrique, Appendice, Bull. Soc. Math. France 86 (1958), 177-251. | Numdam | MR | Zbl

[6] C. Chevalley, Théorie des Groupes de Lie, tome II (Groupes Algébriques), Hermann, Paris, 1951. | Zbl

[7] C. Chevalley, The construction and study of certain important algebras, The Mathematical Society of Japan, Tokyo, 1955. | MR | Zbl

[8] C. Chevalley, Fundamental concepts of algebra, Academic Press Inc., New York, 1956. | MR | Zbl

[9] A. Dold, Les foncteurs dérivés d'un foncteur non-additif, Séminaire Bourbaki, 1958-1959, Exposé 170. | Numdam | Zbl

[10] A. Dold, Homology of symmetric products and other functors of complexes, Ann. of Math. 68 (1958), 54-80. | MR | Zbl

[11] A. Dold and D. Puppe, Non-additive functors, their derived functors and the suspension homomorphism, Proc. Nat. Ac. Sc. USA 44 (1958), 1065-1068. | Zbl

[12] A. Dold und D. Puppe, Homologie nicht-additiver Funktoren, Anwendungen, Annales Inst. Fourier, 11 (1961), 201-312. | Numdam | MR | Zbl

[13] G. Glaeser, Théorie intrinsèque des polynômes et dualité, Bull. Sc. Math., 85 (1961), 17-28. | MR | Zbl

[14] A. Grothendieck et J. Dieudonné, Éléments de Géométrie Algébrique I, Publications Math. de l'IHES n. 4, Paris, 1960. | Numdam

[15] J. L. Koszul, Algebra Multilinear, Sociedade de Matemática de São Paulo, São Paulo, 1956.

[16] F. S. Macaulay, The algebraic theory of modular systems, Cambridge Tracts n. 19, Cambridge University Press, 1916. | JFM | Zbl

[17] A. Micali, Algèbre symétrique d'un idéal, C.R. Acad. Sci, 251 (1960), 1954-1956. | MR | Zbl

[18] A. Micali, Algèbre symétrique d'un module unitaire, C.R. Acad. Sci, 252 (1961), 2658-2660 et 2803-2804. | MR | Zbl

[19] A. Micali, Algèbre de Rees d'un module unitaire, C.R. Acad. Sci, 252 (1961), 3181-3183. | MR | Zbl

[20] A. Micali, Sur les algèbres symétrique et extérieure d'un module projectif, C.R. Acad. Sci, 255 (1962), 2871-2873. | MR | Zbl

[21] D. G. Northcott, Ideal Theory, Cambridge University Press, 1953. | MR | Zbl

[22] D. G. Northcott, An introduction to Homological Algebra, Cambridge University Press, 1960. | MR | Zbl

[23] D. Rees, Two classical theorems of Ideal Theory, Proc. Cambridge Phil. Soc., 52 (1956), 155-157. | MR | Zbl

[24] P. Ribenboim, Anneaux de Rees intégralement clos, Journal R. und A. Math. 204 (1960), 99-107. | MR | Zbl

[25] P. Samuel, P. Salmon et A. Micali, Intégrité et factorialité des algèbres symétriques, Atas do 4o Coloquio Brasileiro de Matemática, Poços de Caldas 1963, à paraître. | Zbl

[26] P. Samuel, Sur les anneaux factoriels, Bull. Soc. Math. France 89 (1961), 155-173. | Numdam | MR | Zbl

[27] O. Zariski and P. Samuel, Commutative Algebra, Van Nostrand, New York, vol. I (1958) and vol. II (1960). | Zbl

  • Höring, Andreas; Peternell, Thomas A Nonvanishing Conjecture for Cotangent Bundles, Annales de la Faculté des sciences de Toulouse : Mathématiques, Volume 32 (2024) no. 5, p. 855 | DOI:10.5802/afst.1756
  • Brion, Michel; Schröer, Stefan The Inverse Galois Problem for Connected Algebraic Groups, Transformation Groups (2024) | DOI:10.1007/s00031-024-09865-0
  • Lorenzini, Dino; Schröer, Stefan Discriminant groups of wild cyclic quotient singularities, Algebra Number Theory, Volume 17 (2023) no. 5, p. 1017 | DOI:10.2140/ant.2023.17.1017
  • Höring, Andreas; Liu, Jie Fano manifolds with big tangent bundle: a characterisation of V5, Collectanea Mathematica, Volume 74 (2023) no. 3, p. 639 | DOI:10.1007/s13348-022-00368-3
  • Aluffi, Paolo Segre Classes and Invariants of Singular Varieties, Handbook of Geometry and Topology of Singularities III (2022), p. 419 | DOI:10.1007/978-3-030-95760-5_6
  • Cid-Ruiz, Yairon A D-modules approach on the equations of the Rees algebra, Journal of Commutative Algebra, Volume 14 (2022) no. 2 | DOI:10.1216/jca.2022.14.155
  • Wu, Xiaojun Strongly Pseudo-Effective and Numerically Flat Reflexive Sheaves, The Journal of Geometric Analysis, Volume 32 (2022) no. 4 | DOI:10.1007/s12220-021-00865-0
  • Annala, Toni Precobordism and cobordism, Algebra Number Theory, Volume 15 (2021) no. 10, p. 2571 | DOI:10.2140/ant.2021.15.2571
  • Busé, Laurent; Chardin, Marc Fibers of Rational Maps and Elimination Matrices: An Application Oriented Approach, Commutative Algebra (2021), p. 189 | DOI:10.1007/978-3-030-89694-2_6
  • Busé, Laurent; Cid‐Ruiz, Yairon; D'Andrea, Carlos Degree and birationality of multi‐graded rational maps, Proceedings of the London Mathematical Society, Volume 121 (2020) no. 4, p. 743 | DOI:10.1112/plms.12336
  • Kerz, Moritz; Strunk, Florian; Tamme, Georg Algebraic K-theory and descent for blow-ups, Inventiones mathematicae, Volume 211 (2018) no. 2, p. 523 | DOI:10.1007/s00222-017-0752-2
  • Andreas, Björn; Sánchez Gómez, Darío; Sancho de Salas, Fernando Euler sequence and Koszul complex of a module, Arkiv för Matematik, Volume 54 (2016) no. 2, p. 277 | DOI:10.1007/s11512-016-0236-4
  • Lin, Kuei-Nuan Cohen–Macaulayness of Rees Algebras of Modules, Communications in Algebra, Volume 44 (2016) no. 9, p. 3673 | DOI:10.1080/00927872.2015.1086925
  • Ramos, Zaqueu; Simis, Aron An analogue of the Aluffi algebra for modules, Journal of Algebra, Volume 467 (2016), p. 155 | DOI:10.1016/j.jalgebra.2016.07.027
  • Narváez Macarro, Luis A duality approach to the symmetry of Bernstein–Sato polynomials of free divisors, Advances in Mathematics, Volume 281 (2015), p. 1242 | DOI:10.1016/j.aim.2015.06.012
  • Fouli, Louiza; Lin, Kuei-Nuan Rees algebras of square-free monomial ideals, Journal of Commutative Algebra, Volume 7 (2015) no. 1 | DOI:10.1216/jca-2015-7-1-25
  • Imbesi, Maurizio Integrality of the symmetric algebra of graph ideals, Mathematical Notes, Volume 94 (2013) no. 1-2, p. 191 | DOI:10.1134/s0001434613070195
  • Имбеси; Imbesi Целостность симметрических алгебр идеалов графов, Математические заметки, Volume 94 (2013) no. 2, p. 190 | DOI:10.4213/mzm10290
  • KULOSMAN, HAMID COMPARISON OF c AND d-SEQUENCES, Journal of Algebra and Its Applications, Volume 11 (2012) no. 01, p. 1250010 | DOI:10.1142/s0219498811005336
  • Branco Correia, Ana L.; Zarzuela, Santiago On Equimultiple Modules, Communications in Algebra, Volume 37 (2009) no. 6, p. 1949 | DOI:10.1080/00927870802255675
  • O'Carroll, Liam; Planas-Vilanova, Francesc Irreducible affine space curves and the uniform Artin–Rees property on the prime spectrum, Journal of Algebra, Volume 320 (2008) no. 8, p. 3339 | DOI:10.1016/j.jalgebra.2008.06.029
  • Giral, José M.; Planas-Vilanova, Francesc A note on the acyclicity of the Koszul complex of a module, Arkiv för Matematik, Volume 45 (2007) no. 2, p. 273 | DOI:10.1007/s11512-007-0043-z
  • Picavet, Gabriel Absolutely integral homomorphisms, Journal of Algebra, Volume 311 (2007) no. 2, p. 584 | DOI:10.1016/j.jalgebra.2006.12.011
  • Branco Correia, Ana L.; Zarzuela, Santiago On the asymptotic properties of the Rees powers of a module, Journal of Pure and Applied Algebra, Volume 207 (2006) no. 2, p. 373 | DOI:10.1016/j.jpaa.2005.10.012
  • Aluffi, Paolo Shadows of blow-up algebras, Tohoku Mathematical Journal, Volume 56 (2004) no. 4 | DOI:10.2748/tmj/1113246753
  • Aluffi, Paolo Computing characteristic classes of projective schemes, Journal of Symbolic Computation, Volume 35 (2003) no. 1, p. 3 | DOI:10.1016/s0747-7171(02)00089-5
  • Picavet, Gabriel Algebraically flat or projective algebras, Journal of Pure and Applied Algebra, Volume 174 (2002) no. 2, p. 163 | DOI:10.1016/s0022-4049(02)00048-8
  • Kaliman, Sh.; Zaidenberg, M. Affine modifications and affine hypersurfaces with a very transitive automorphism group, Transformation Groups, Volume 4 (1999) no. 1, p. 53 | DOI:10.1007/bf01236662
  • Barile, Margherita; Morales, Marcel On Certain Algebras of Reduction Number One, Journal of Algebra, Volume 206 (1998) no. 1, p. 113 | DOI:10.1006/jabr.1997.7414
  • Katz, D.; Ratliff, L.J. Sequences and Ker(R[X1,…,Xg] → R[tl]), Journal of Pure and Applied Algebra, Volume 122 (1997) no. 3, p. 265 | DOI:10.1016/s0022-4049(97)00058-3
  • Restuccia, Gaetana; Ionescu, Cristodor q-Torsion freeness of symmetric powers, Rendiconti del Circolo Matematico di Palermo, Volume 46 (1997) no. 3, p. 329 | DOI:10.1007/bf02844276
  • Blanco, Amalia; Majadas, Javier Sur l'annulation de la cohomologie de hochschild des anneaux de gorenstein, Communications in Algebra, Volume 24 (1996) no. 5, p. 1777 | DOI:10.1080/00927879608825670
  • Yoshida, Ken-ichi Cohen-macaulay symmetric algebras with maximal embedding dimension of almost complete intersection ideals, Communications in Algebra, Volume 23 (1995) no. 2, p. 653 | DOI:10.1080/00927879508825240
  • Keel, Sean Intersection theory of linear embeddings, Transactions of the American Mathematical Society, Volume 335 (1993) no. 1, p. 195 | DOI:10.1090/s0002-9947-1993-1040263-6
  • Raghavan, K.N. A simple proof that ideals generated by d-sequences are of linear type, Communications in Algebra, Volume 19 (1991) no. 10, p. 2827 | DOI:10.1080/00927879108824295
  • Kotzev, Boris V Determinantal ideals of linear type of a generic symmetric matrix, Journal of Algebra, Volume 139 (1991) no. 2, p. 484 | DOI:10.1016/0021-8693(91)90305-r
  • Vasconcelos, Wolmer V. Symmetric algebras, Commutative Algebra, Volume 1430 (1990), p. 115 | DOI:10.1007/bfb0085540
  • Huckaba, Sam On complete d-sequences and the defining ideals of Rees algebras, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 106 (1989) no. 3, p. 445 | DOI:10.1017/s0305004100068183
  • Rossi, M.E.; Valla, G. Multiplicity andt-isomultiple ideals, Nagoya Mathematical Journal, Volume 110 (1988), p. 81 | DOI:10.1017/s0027763000002889
  • Huckaba, Sam Reduction numbers for ideals of higher analytic spread, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 102 (1987) no. 01, p. 49 | DOI:10.1017/s0305004100067037
  • Huneke, Craig Determinantal ideals of linear type, Archiv der Mathematik, Volume 47 (1986) no. 4, p. 324 | DOI:10.1007/bf01191358
  • Agawany, Mohamed El; Micali, Arribano Algébre mèsonique d’un module, Communications in Algebra, Volume 13 (1985) no. 2, p. 399 | DOI:10.1080/00927878508823167
  • Escamilla-Castillo, Juan Algèbres Symétriques et Singularités, ANNALI DELL UNIVERSITA DI FERRARA, Volume 30 (1984) no. 1, p. 1 | DOI:10.1007/bf02853265
  • Evelina Rossi, Maria A note on the symmetric algebras which are gorenstein rings, Communications in Algebra, Volume 11 (1983) no. 22, p. 2575 | DOI:10.1080/00927878308822981
  • Costa, Douglas L On the torsion-freeness of the symmetric powers of an ideal, Journal of Algebra, Volume 80 (1983) no. 1, p. 152 | DOI:10.1016/0021-8693(83)90024-8
  • Rossi, Maria Evelina On the cohen-macaulay type of the symmetric algebra of a local ring, Communications in Algebra, Volume 10 (1982) no. 9, p. 981 | DOI:10.1080/00927878208822760
  • Rossi, Maria Evelina On symmetric algebras which are Cohen Macaulay, Manuscripta Mathematica, Volume 34 (1981) no. 2-3, p. 199 | DOI:10.1007/bf01165536
  • Valla, Giuseppe On the Symmetric and Rees algebras of an ideal, Manuscripta Mathematica, Volume 30 (1979) no. 3, p. 239 | DOI:10.1007/bf01303330
  • Costa, Roberto; Micali, Artibano Sur les algebres de Rees II, Manuscripta Mathematica, Volume 26 (1978) no. 1-2, p. 1 | DOI:10.1007/bf01167964
  • Valla, G Certain graded algebras are always Cohen-Macaulay, Journal of Algebra, Volume 42 (1976) no. 2, p. 537 | DOI:10.1016/0021-8693(76)90112-5
  • Rhodes, C. P. L. A multiplicative property of R-sequences and H1-sets, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 78 (1975) no. 1, p. 1 | DOI:10.1017/s030500410005146x
  • Barshay, Jacob Graded algebras of powers of ideals generated by A-sequences, Journal of Algebra, Volume 25 (1973) no. 1, p. 90 | DOI:10.1016/0021-8693(73)90076-8
  • Wolffhardt, Klaus The Hochschild homology of complete intersections, Transactions of the American Mathematical Society, Volume 171 (1972) no. 0, p. 51 | DOI:10.1090/s0002-9947-1972-0306192-4
  • Micali, Artibano; Roby, Norbert Algèbres symétriques et syzygies, Journal of Algebra, Volume 17 (1971) no. 4, p. 460 | DOI:10.1016/0021-8693(71)90002-0
  • Barshay, Jacob A characterization of regular local rings, Proceedings of the American Mathematical Society, Volume 29 (1971) no. 3, p. 437 | DOI:10.1090/s0002-9939-1971-0279093-2

Cité par 55 documents. Sources : Crossref