Minimal injective resolutions with applications to dualizing modules and Gorenstein modules
Publications Mathématiques de l'IHÉS, Volume 45  (1975), p. 193-215
@article{PMIHES_1975__45__193_0,
     author = {Fossum, Robert M. and Foxby, Hans-Bjorn and Griffith, Phillip A. and Reiten, Idun},
     title = {Minimal injective resolutions with applications to dualizing modules and Gorenstein modules},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {45},
     year = {1975},
     pages = {193-215},
     zbl = {0321.13013},
     mrnumber = {53 \#392},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1975__45__193_0}
}
Fossum, Robert; Foxby, Hans-Bjorn; Griffith, Phillip; Reiten, Idun. Minimal injective resolutions with applications to dualizing modules and Gorenstein modules. Publications Mathématiques de l'IHÉS, Volume 45 (1975) , pp. 193-215. http://www.numdam.org/item/PMIHES_1975__45__193_0/

[1] M. Auslander and M. Bridger, Stable module theory, Memoirs Amer. Math. Soc., no. 94 (1969). | MR 42 #4580 | Zbl 0204.36402

[2] M. Auslander and D. Buchsbaum, Homological dimension in local rings, II, Trans. Amer. Math. Soc., 85 (1957), 390-405. | MR 19,249d | Zbl 0078.02802

[3] M. Auslander and O. Goldman, The Brauer group of a commutative ring, Trans. Amer. Math. Soc., 97 (1960), 367-409. | MR 22 #12130 | Zbl 0100.26304

[4] G. Azumaya, On maximally central algebras, Nagoya Math. J., 2 (1951), 119-150. | MR 12,669g | Zbl 0045.01103

[5] H. Bass, On the ubiquity of Gorenstein rings, Math. Z., 82 (1963), 8-28. | MR 27 #3669 | Zbl 0112.26604

[6] M.-J. Bertin, Anneaux d'invariants d'anneaux de polynômes, en caractéristique p, C. R. Acad. Sci. Paris, 264 (1967), 653-656. | MR 35 #6661 | Zbl 0147.29503

[7] H. Cartan and S. Eilenberg, Homological Algebra, Princeton University Press, 1956. | MR 17,1040e | Zbl 0075.24305

[8] I. S. Cohen, On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc., 59 (1946), 54-106. | MR 7,509h | Zbl 0060.07001

[9] J. A. Eagon and D. G. Northcott, Ideals defined by matrices and a certain complex associated with them, Proc. Royal Soc. A, 269 (1962), 188-204. | MR 26 #161 | Zbl 0106.25603

[10] J. A. Eagon, Examples of Cohen-Macaulay rings which are not Gorenstein, Math. Z., 109 (1969), 109-111. | MR 39 #5552 | Zbl 0184.29201

[11] D. Ferrand and M. Raynaud, Fibres formelles d'un anneau local noethérien, Ann. Sci. Éc. Norm. Sup. (4), 3 (1970), 295-311. | Numdam | MR 42 #7660 | Zbl 0204.36601

[12] R. Fossum and P. Griffith, A complete local factorial ring of dimension 4 which is not Cohen-Macaulay, Bull. Amer. Math. Soc., 81 (1975), 111-113. | MR 50 #9858 | Zbl 0301.13006

[13] R. Fossum, P. Griffith and I. Reiten, Trivial Extensions of Abelian Categories, Lecture Notes in Mathematics, No. 456, Berlin-Heidelberg-New York, Springer-Verlag, 1975. | MR 52 #10810 | Zbl 0303.18006

[14] H.-B. Foxby, On the ui in a minimal injective resolution, Math. Scand., 29 (1971), 175-186. | MR 46 #9023 | Zbl 0235.13006

[15] H.-B. Foxby, Gorenstein modules and related modules, Math. Scand., 31 (1972), 367-384. | MR 48 #6094 | Zbl 0272.13009

[16] H.-B. Foxby, n-Gorenstein rings, Proc. Amer. Math. Soc., 42 (1974), 67-72. | MR 48 #2140 | Zbl 0294.13015

[17] P. Gabriel, Des catégories abéliennes, Bull. Soc. Math. France, 90 (1963), 323-448. | Numdam | MR 38 #1144 | Zbl 0201.35602

[18] A. Grothendieck, Théorèmes de dualité pour les faisceaux algébriques cohérents, Séminaire Bourbaki, Exp. 149, Mai 1957. | Numdam

[19] A. Grothendieck, Local Cohomology, Lecture Notes in Mathematics, No. 41, Berlin-Heidelberg-New York, Springer 1967. | MR 37 #219 | Zbl 0185.49202

[20] A. Grothendieck, Le groupe de Brauer, I, Dix Exposés sur la cohomologie des schémas, Amsterdam, North-Holland Pub. Co. (1969), 46-65. | Zbl 0193.21503

[21] T. Gulliksen, Massey operations and the Poincaré series of certain local rings, J. Algebra, 22 (1972), 223-232. | MR 46 #5317 | Zbl 0243.13015

[22] R. Hartshorne, Residues and duality, Lecture Notes in Mathematics, No. 20, Berlin-Heidelberg-New York, Springer, 1966. | MR 36 #5145 | Zbl 0212.26101

[23] R. Hartshorne and A. Ogus, On the factoriality of local rings of small embedding codimension, Communications in Algebra, 1 (1974), 415-437. | MR 50 #322 | Zbl 0286.13013

[24] J. Herzog and E. Kunz, Der kanonische Modul eines Cohen-Macaulay-Rings, Lecture Notes in Mathematics, No. 238, Berlin-Heidelberg-New York, Springer, 1971. | MR 54 #304 | Zbl 0231.13009

[25] M. Hochster, Deep local rings, Preprint Series No. 8 (1973/1974), Aarhus, Denmark, Aarhus Universitets Mathematiske Institut.

[26] Birger Iversen, Generic Local Structure in Commutative Algebra, Lecture Notes in Mathematics, No. 310, Berlin-Heidelberg-New York, Springer, 1973. | MR 50 #13023 | Zbl 0247.13001

[27] I. Kaplansky, Commutative Rings, Boston, Allyn and Bacon, Inc., 1970. | MR 40 #7234 | Zbl 0203.34601

[28] M.-A. Knus and M. Ojanguren, Sur quelques applications de la théorie de la descente à l'étude du groupe de Brauer, Comm. Math. Helv., 47 (1972), 532-542. | MR 50 #2146 | Zbl 0248.13002

[29] E. Matlis, Injective modules over noetherian rings, Pacific J. Math., 8 (1958), 511-528. | MR 20 #5800 | Zbl 0084.26601

[30] H. Matsumura, Commutative Algebra, New York, W. A. Benjamin, Inc., 1970. | MR 42 #1813 | Zbl 0211.06501

[31] M. P. Murthy, A note on factorial rings, Arch. Math., 15 (1964), 418-420. | MR 30 #3905 | Zbl 0123.03401

[32] D. G. Northcott, Some remarks on the theory of ideals defined by matrices, Quart. J. Math. Oxford (2), 14 (1963), 193-204. | MR 27 #1467 | Zbl 0116.02504

[33] C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale, Publ. Math. I.H.E.S., 42 (1973), 49-119. | Numdam | Zbl 0268.13008

[34] I. Reiten, The converse to a theorem of Sharp on Gorenstein modules, Proc. Amer. Math. Soc., 32 (1972), 417-420. | MR 45 #5128 | Zbl 0235.13016

[35] I. Reiten and R. Fossum, Commutative n-Gorenstein rings, Math. Scand., 31 (1972), 33-48. | MR 51 #12839 | Zbl 0256.13016

[36] J.-E. Roos, Sur les dérivés de limATT. Applications, C. R. Acad. Sci. Paris, 252 (1961), 3702-3704. | MR 24 #A1938 | Zbl 0102.02501

[37] R. Y. Sharp, Gorenstein modules, Math. Z., 115 (1970), 117-139. | MR 41 #8401 | Zbl 0186.07403

[38] R. Y. Sharp, Finitely generated modules of finite injective dimension over certain Cohen-Macaulay rings, Proc. London Math. Soc., 25 (1972), 303-328. | MR 46 #5315 | Zbl 0244.13015

[39] R. Y. Sharp, On Gorenstein modules over a complete Cohen-Macaulay local ring, Quart. J. Math. (Oxford) (2), 22 (1971), 425-434. | MR 44 #6693 | Zbl 0221.13016

[40] R. Y. Sharp, The Cousin complex for a module over a commutative Noetherian ring, Math. Z., 112 (1969), 340-356. | MR 41 #8400 | Zbl 0182.06103

[41] R. Y. Sharp, The Euler characteristic of a finitely generated module of finite injective dimension, Math. Z., 130 (1973), 79-93. | MR 47 #8518 | Zbl 0237.13009