@article{PMIHES_1975__45__193_0, author = {Fossum, Robert and Foxby, Hans-Bjorn and Griffith, Phillip and Reiten, Idun}, title = {Minimal injective resolutions with applications to dualizing modules and {Gorenstein} modules}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {193--215}, publisher = {Institut des Hautes \'Etudes Scientifiques}, volume = {45}, year = {1975}, mrnumber = {53 #392}, zbl = {0321.13013}, language = {en}, url = {http://www.numdam.org/item/PMIHES_1975__45__193_0/} }
TY - JOUR AU - Fossum, Robert AU - Foxby, Hans-Bjorn AU - Griffith, Phillip AU - Reiten, Idun TI - Minimal injective resolutions with applications to dualizing modules and Gorenstein modules JO - Publications Mathématiques de l'IHÉS PY - 1975 SP - 193 EP - 215 VL - 45 PB - Institut des Hautes Études Scientifiques UR - http://www.numdam.org/item/PMIHES_1975__45__193_0/ LA - en ID - PMIHES_1975__45__193_0 ER -
%0 Journal Article %A Fossum, Robert %A Foxby, Hans-Bjorn %A Griffith, Phillip %A Reiten, Idun %T Minimal injective resolutions with applications to dualizing modules and Gorenstein modules %J Publications Mathématiques de l'IHÉS %D 1975 %P 193-215 %V 45 %I Institut des Hautes Études Scientifiques %U http://www.numdam.org/item/PMIHES_1975__45__193_0/ %G en %F 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, Tome 45 (1975), pp. 193-215. http://www.numdam.org/item/PMIHES_1975__45__193_0/
[1] Stable module theory, Memoirs Amer. Math. Soc., no. 94 (1969). | MR | Zbl
and ,[2] Homological dimension in local rings, II, Trans. Amer. Math. Soc., 85 (1957), 390-405. | MR | Zbl
and ,[3] The Brauer group of a commutative ring, Trans. Amer. Math. Soc., 97 (1960), 367-409. | MR | Zbl
and ,[4] On maximally central algebras, Nagoya Math. J., 2 (1951), 119-150. | MR | Zbl
,[5] On the ubiquity of Gorenstein rings, Math. Z., 82 (1963), 8-28. | MR | Zbl
,[6] Anneaux d'invariants d'anneaux de polynômes, en caractéristique p, C. R. Acad. Sci. Paris, 264 (1967), 653-656. | MR | Zbl
,[7] Homological Algebra, Princeton University Press, 1956. | MR | Zbl
and ,[8] On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc., 59 (1946), 54-106. | MR | Zbl
,[9] Ideals defined by matrices and a certain complex associated with them, Proc. Royal Soc. A, 269 (1962), 188-204. | MR | Zbl
and ,[10] Examples of Cohen-Macaulay rings which are not Gorenstein, Math. Z., 109 (1969), 109-111. | MR | Zbl
,[11] Fibres formelles d'un anneau local noethérien, Ann. Sci. Éc. Norm. Sup. (4), 3 (1970), 295-311. | Numdam | MR | Zbl
and ,[12] A complete local factorial ring of dimension 4 which is not Cohen-Macaulay, Bull. Amer. Math. Soc., 81 (1975), 111-113. | MR | Zbl
and ,[13] Trivial Extensions of Abelian Categories, Lecture Notes in Mathematics, No. 456, Berlin-Heidelberg-New York, Springer-Verlag, 1975. | MR | Zbl
, and ,[14] On the ui in a minimal injective resolution, Math. Scand., 29 (1971), 175-186. | MR | Zbl
,[15] Gorenstein modules and related modules, Math. Scand., 31 (1972), 367-384. | MR | Zbl
,[16] n-Gorenstein rings, Proc. Amer. Math. Soc., 42 (1974), 67-72. | MR | Zbl
,[17] Des catégories abéliennes, Bull. Soc. Math. France, 90 (1963), 323-448. | Numdam | MR | Zbl
,[18] Théorèmes de dualité pour les faisceaux algébriques cohérents, Séminaire Bourbaki, Exp. 149, Mai 1957. | Numdam
,[19] Local Cohomology, Lecture Notes in Mathematics, No. 41, Berlin-Heidelberg-New York, Springer 1967. | MR | Zbl
,[20] Le groupe de Brauer, I, Dix Exposés sur la cohomologie des schémas, Amsterdam, North-Holland Pub. Co. (1969), 46-65. | Zbl
,[21] Massey operations and the Poincaré series of certain local rings, J. Algebra, 22 (1972), 223-232. | MR | Zbl
,[22] Residues and duality, Lecture Notes in Mathematics, No. 20, Berlin-Heidelberg-New York, Springer, 1966. | MR | Zbl
,[23] On the factoriality of local rings of small embedding codimension, Communications in Algebra, 1 (1974), 415-437. | MR | Zbl
and ,[24] Der kanonische Modul eines Cohen-Macaulay-Rings, Lecture Notes in Mathematics, No. 238, Berlin-Heidelberg-New York, Springer, 1971. | MR | Zbl
and ,[25] Deep local rings, Preprint Series No. 8 (1973/1974), Aarhus, Denmark, Aarhus Universitets Mathematiske Institut.
,[26] Generic Local Structure in Commutative Algebra, Lecture Notes in Mathematics, No. 310, Berlin-Heidelberg-New York, Springer, 1973. | MR | Zbl
,[27] Commutative Rings, Boston, Allyn and Bacon, Inc., 1970. | MR | Zbl
,[28] Sur quelques applications de la théorie de la descente à l'étude du groupe de Brauer, Comm. Math. Helv., 47 (1972), 532-542. | MR | Zbl
and ,[29] Injective modules over noetherian rings, Pacific J. Math., 8 (1958), 511-528. | MR | Zbl
,[30] Commutative Algebra, New York, W. A. Benjamin, Inc., 1970. | MR | Zbl
,[31] A note on factorial rings, Arch. Math., 15 (1964), 418-420. | MR | Zbl
,[32] Some remarks on the theory of ideals defined by matrices, Quart. J. Math. Oxford (2), 14 (1963), 193-204. | MR | Zbl
,[33] Dimension projective finie et cohomologie locale, Publ. Math. I.H.E.S., 42 (1973), 49-119. | Numdam | Zbl
and ,[34] The converse to a theorem of Sharp on Gorenstein modules, Proc. Amer. Math. Soc., 32 (1972), 417-420. | MR | Zbl
,[35] Commutative n-Gorenstein rings, Math. Scand., 31 (1972), 33-48. | MR | Zbl
and ,[36] Sur les dérivés de lim. Applications, C. R. Acad. Sci. Paris, 252 (1961), 3702-3704. | MR | Zbl
,[37] Gorenstein modules, Math. Z., 115 (1970), 117-139. | MR | Zbl
,[38] Finitely generated modules of finite injective dimension over certain Cohen-Macaulay rings, Proc. London Math. Soc., 25 (1972), 303-328. | MR | Zbl
,[39] On Gorenstein modules over a complete Cohen-Macaulay local ring, Quart. J. Math. (Oxford) (2), 22 (1971), 425-434. | MR | Zbl
,[40] The Cousin complex for a module over a commutative Noetherian ring, Math. Z., 112 (1969), 340-356. | MR | Zbl
,[41] The Euler characteristic of a finitely generated module of finite injective dimension, Math. Z., 130 (1973), 79-93. | MR | Zbl
,