Geodesic
Fitting Conditions for Symmetric Algebras of Modules of Finite Projective Dimension
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 681-696.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Let $E$ be a finitely generated $R$-module, having finite projective dimension. We study the acyclicity of the approximation complex $\mathcal{Z}(E)$ of $E$ in terms of certain Fitting conditions $F_k^{(i)}$ on the Fitting ideals of the $i$-th module of a projective resolution of $E$. We deduce some good properties of the symmetric algebra of $E$.
Sia $E$ un $R$-modulo finitamente generato, di dimensione proiettiva finita. Studiamo l'aciclicità del complesso di approssimazione $\mathcal{Z}(E)$ di $E$ in termini di certe condizioni Fitting $F_k^{(i)}$ sugli ideali Fitting dell'$i$-esimo modulo di una risoluzione proiettiva di $E$. Ne deduciamo alcune buone proprietà dell'algebra simmetrica di $E$. 
@article{BUMI_2007_8_10B_3_a13,
     author = {Ionescu, Cristodor and Restuccia, Gaetana and Utano, Rosanna},
     title = {Fitting {Conditions} for {Symmetric} {Algebras} of {Modules} of {Finite} {Projective} {Dimension}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {681--696},
     publisher = {mathdoc},
     volume = {Ser. 8, 10B},
     number = {3},
     year = {2007},
     zbl = {1177.13021},
     mrnumber = {2351537},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a13/}
}
TY  - JOUR
AU  - Ionescu, Cristodor
AU  - Restuccia, Gaetana
AU  - Utano, Rosanna
TI  - Fitting Conditions for Symmetric Algebras of Modules of Finite Projective Dimension
JO  - Bollettino della Unione matematica italiana
PY  - 2007
SP  - 681
EP  - 696
VL  - 10B
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a13/
LA  - en
ID  - BUMI_2007_8_10B_3_a13
ER  - 
%0 Journal Article
%A Ionescu, Cristodor
%A Restuccia, Gaetana
%A Utano, Rosanna
%T Fitting Conditions for Symmetric Algebras of Modules of Finite Projective Dimension
%J Bollettino della Unione matematica italiana
%D 2007
%P 681-696
%V 10B
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a13/
%G en
%F BUMI_2007_8_10B_3_a13
Ionescu, Cristodor; Restuccia, Gaetana; Utano, Rosanna. Fitting Conditions for Symmetric Algebras of Modules of Finite Projective Dimension. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 681-696. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a13/

[1] L. L. Avramov, Complete intersections and symmetric algebras, J. Algebra, 73 (1981), 248-263. | DOI | MR | Zbl

[2] M. Auslander - M. Bridger, Stable module theory, Mem. Amer. Math. Soc. 94 (1969). | MR | Zbl

[3] D. Buchsbaum - D. Eisenbud, What makes a complex exact?, J. Algebra, 25 (1973), 259-268. | DOI | MR | Zbl

[4] W. Bruns - J. Herzog, Cohen-Macaulay rings, Cambridge University Press, Cambridge, 1998. | MR

[5] D. Eisenbud - C. Huneke - B. Ulrich, Heights of ideals of minors, Amer. J. Math., 126 (2004), 417-438. | MR | Zbl

[6] J. Eagon - D. G. Northcott, Ideals defined by matrices and a certain complex associated with them, Proc. Royal Soc. London Ser. A, 269 (1962), 188-204. | MR | Zbl

[7] J. Herzog - A. Simis - W. V. Vasconcelos, On the arithmetic and homology of algebras of linear type, Trans. Amer. Math. Soc., 283 (1984), 661-683. | DOI | MR | Zbl

[8] J. Herzog - A. Simis - W. V. Vasconcelos, Koszul homology and blowing-up rings, Commutative algebra (Trento, 1981), pp. 79-169, Lecture Notes in Pure and Appl. Math., 84, Dekker, New York, 1983. | MR | Zbl

[9] M. Kühl, On the symmetric algebra of an ideal, Manuscripta Math., 37 (1982), 49-60. | fulltext EuDML | DOI | MR

[10] K. Lebelt, Freie Auflösungen äuerer Potenzen, Manuscripta Math., 21 (1977), 341- 355. | fulltext EuDML | DOI | MR

[11] G. Molica - G. Restuccia, Torsion free exterior powers of a module and their resolutions, An. Şt. Univ. Ovidius Constanta, 10 (2002), 101-108. | fulltext EuDML | MR | Zbl

[12] G. Restuccia, On the ideal of relations of a symmetric algebra, Rend. Sem. Mat. Univers. Politecn. Torino, 49 (1991), 281-298. | MR | Zbl

[13] G. Restuccia, On the symmetric algebra for a module of projective dimension two, An. St. Univ. Bucarest Mat., 40 (1991), 83-91. | MR | Zbl

[14] G. Restuccia - C. Ionescu, q-torsion freeness of symmetric powers, Rend. Circ. Mat. Palermo, XLVI (1997), 329-346. | DOI | MR | Zbl

[15] A. Simis - W. V. Vasconcelos, The syzygies of the conormal module, Amer. J. Math. 103 (1981), 203-224. | DOI | MR | Zbl

[16] R. Utano - G. Restuccia, Integrity of the symmetric algebra of modules of projective dimension two, Riv. Mat. Univ. Parma, 4 (1995), 193-204. | MR | Zbl

[17] A. B. Tchernev, Acyclicity of symmetric and exterior powers of complexes, J. Algebra, 184 (1996), 1113-1135. | DOI | MR | Zbl

[18] W. V. Vasconcelos, On linear complete intersections, J. Algebra, 111 (1987), 306- 315. | DOI | MR | Zbl

[19] W. V. Vasconcelos, Symmetric algebras, Lect. Notes in Math., 1430 (1988), 115-160. | DOI | MR

[20] J. Weyman, Resolutions of the exterior and symmetric powers of a module, J. Algebra, 58 (1979), 333-341. | DOI | MR | Zbl