Geodesic
REFLEXIVITY AND CONNECTEDNESS
Glasgow mathematical journal, Tome 57 (2015) no. 1, pp. 231-240

Voir la notice de l'article provenant de la source Cambridge University Press

Given a finitely generated module over a commutative noetherian ring that satisfies certain reflexivity conditions, we show how failure of the semidualizing property for the module manifests in a disconnection of the prime spectrum of the ring.
DOI : 10.1017/S0017089514000354
Mots-clés : 13D02, 13D07, 13D09, 13G05 
SATHER-WAGSTAFF, SEAN. REFLEXIVITY AND CONNECTEDNESS. Glasgow mathematical journal, Tome 57 (2015) no. 1, pp. 231-240. doi: 10.1017/S0017089514000354
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[1] 1.Atiyah, M. F. and Macdonald, I. G., Introduction to commutative algebra (Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969). MR 0242802 (39#4129) Google Scholar

[2] 2.Auslander, M., Anneaux de Gorenstein, et torsion en algèbre commutative, Séminaire d'Algèbre Commutative dirigé par Pierre Samuel, vol. 1966/67, (Secrétariat mathématique, Paris, 1967). MR 37 #1435 Google Scholar

[3] 3.Auslander, M. and Bridger, M., Stable module theory, Memoirs of the American Mathematical Society, vol. 94 (American Mathematical Society, Providence, R.I., 1969). MR 42 #4580 Google Scholar

[4] 4.Avramov, L. L. and Foxby, H.-B., Ring homomorphisms and finite Gorenstein dimension, Proc. London Math. Soc. 75 (3) (1997), 241–270. MR 98d:13014 Google Scholar

[5] 5.Avramov, L. L., Iyengar, S. B. and Lipman, J., Reflexivity and rigidity for complexes. I. Commutative rings, Algebra Number Theory 4 (1) (2010), 47–86. MR 2592013 Google Scholar | DOI

[6] 6.Christensen, L. W., Semi-dualizing complexes and their Auslander categories, Trans. Am. Math. Soc. 353 (5) (2001), 1839–1883. MR 2002a:13017 Google Scholar

[7] 7.Enochs, E. E., Jenda, O. M. G. and Xu, J. Z., Foxby duality and Gorenstein injective and projective modules, Trans. Amer. Math. Soc. 348 (8) (1996), 3223–3234. MR 1355071 (96k:13010) Google Scholar | DOI

[8] 8.Foxby, H.-B., Gorenstein modules and related modules, Math. Scand. 31 (1972), 267–284. MR 48 #6094 Google Scholar

[9] 9.Foxby, H.-B., Gorenstein dimensions over Cohen-Macaulay rings, in Proceedings of the international conference on commutative algebra (Osnabrück, Germany) (Bruns, W., Editor) (Universität Osnabrück, 1994), 59–63. Google Scholar

[10] 10.Frankild, A. and Sather-Wagstaff, S., Reflexivity and ring homomorphisms of finite flat dimension, Commun. Algebra 35 (2) (2007), 461–500. MR 2294611 Google Scholar | DOI

[11] 11.Frankild, A. and Sather-Wagstaff, S., The set of semidualizing complexes is a nontrivial metric space, J. Algebra 308 (1) (2007), 124–143. MR 2290914 Google Scholar

[12] 12.Frankild, A. J., Sather-Wagstaff, S. and Taylor, A., Relations between semidualizing complexes, J. Commut. Algebra 1 (3) (2009), 393–436. MR 2524860 Google Scholar | DOI

[13] 13.Golod, E. S., G-dimension and generalized perfect ideals, Algebraic geometry and its applications, Trudy Mat. Inst. Steklov. 165 (1984), 62–66. MR 85m:13011 Google Scholar

[14] 14.Hartshorne, R., Residues and duality, Lecture Notes in Mathematics, vol. 20 (Springer-Verlag, Berlin, 1966). MR 36 #5145 Google Scholar

[15] 15.Hartshorne, R., Local cohomology, A seminar given by A. Grothendieck, Harvard University, Fall, vol. 1961 (Springer-Verlag, Berlin, 1967). MR 0224620 (37 #219) Google Scholar

[16] 16.Sather-Wagstaff, S., Complete intersection dimensions and Foxby classes, J. Pure Appl. Algebra 212 (12) (2008), 2594–2611. MR 2452313 (2009h:13015) Google Scholar | DOI

[17] 17.Sather-Wagstaff, S., Bass numbers and semidualizing complexes, Commutative Algebra and its Applications (Walter de Gruyter, Berlin, 2009), 349–381. MR 2640315 Google Scholar

[18] 18.Vasconcelos, W. V., Divisor theory in module categories, North-Holland Mathematics Studies, No. 14, Notas de Matemática No. 53. [Notes on Mathematics, No. 53] (North-Holland Publishing Co., Amsterdam, 1974). MR 0498530 (58 #16637) Google Scholar

[19] 19.Yassemi, S., G-dimension, Math. Scand. 77 (2) (1995), 161–174. MR 97d:13017 Google Scholar

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