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Injective dimension in Noetherian rings
Author:
Hyman Bass
Journal:
Trans. Amer. Math. Soc. 102 (1962), 18-29
MSC:
Primary 16.25; Secondary 16.20
MathSciNet review:
0138644
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- [1]
E.
F. Assmus Jr., On the homology of local rings, Illinois J.
Math. 3 (1959), 187–199. MR 0103907
(21 #2670)
- [2]
Maurice
Auslander and David
A. Buchsbaum, Homological dimension in local
rings, Trans. Amer. Math. Soc. 85 (1957), 390–405. MR 0086822
(19,249d), http://dx.doi.org/10.1090/S0002-9947-1957-0086822-7
- [3]
Maurice
Auslander and David
A. Buchsbaum, Homological dimension in noetherian
rings. II, Trans. Amer. Math. Soc. 88 (1958), 194–206. MR 0096720
(20 #3203), http://dx.doi.org/10.1090/S0002-9947-1958-0096720-1
- [4]
Hyman
Bass, Finitistic dimension and a homological
generalization of semi-primary rings, Trans.
Amer. Math. Soc. 95
(1960), 466–488. MR 0157984
(28 #1212), http://dx.doi.org/10.1090/S0002-9947-1960-0157984-8
- [5]
Hyman
Bass, Torsion free and projective
modules, Trans. Amer. Math. Soc. 102 (1962), 319–327. MR 0140542
(25 #3960), http://dx.doi.org/10.1090/S0002-9947-1962-0140542-0
- [6]
Henri
Cartan and Samuel
Eilenberg, Homological algebra, Princeton University Press,
Princeton, N. J., 1956. MR 0077480
(17,1040e)
- [7]
Stephen
U. Chase, Direct products of modules,
Trans. Amer. Math. Soc. 97 (1960), 457–473. MR 0120260
(22 #11017), http://dx.doi.org/10.1090/S0002-9947-1960-0120260-3
- [8]
Jean
Dieudonné, Remarks on quasi-Frobenius rings, Illinois
J. Math. 2 (1958), 346–354. MR 0097427
(20 #3896)
- [9]
B.
Eckmann and A.
Schopf, Über injektive Moduln, Arch. Math. (Basel)
4 (1953), 75–78 (German). MR 0055978
(15,5d)
- [10]
Samuel
Eilenberg and Tadasi
Nakayama, On the dimension of modules and algebras. II. Frobenius
algebras and quasi-Frobenius rings, Nagoya Math. J. 9
(1955), 1–16. MR 0073577
(17,453a)
- [11]
W.
Gröbner, Ein Irreduzibilitätskriterium für
Primärideale in kommutativen Ringen, Monatsh. Math.
55 (1951), 138–145 (German). MR 0043074
(13,202b)
- [12]
J.
P. Jans, Duality in Noetherian rings,
Proc. Amer. Math. Soc. 12 (1961), 829–835. MR 0137743
(25 #1192), http://dx.doi.org/10.1090/S0002-9939-1961-0137743-9
- [13]
Eben
Matlis, Injective modules over Noetherian rings, Pacific J.
Math. 8 (1958), 511–528. MR 0099360
(20 #5800)
- [14]
Eben
Matlis, Applications of duality, Proc. Amer. Math. Soc. 10 (1959), 659–662. MR 0106937
(21 #5667), http://dx.doi.org/10.1090/S0002-9939-1959-0106937-1
- [15]
D.
G. Northcott and D.
Rees, Extensions and simplifications of the theory or regular local
rings, J. London Math. Soc. 32 (1957), 367–374.
MR
0089189 (19,630f)
- [16]
Oscar
Zariski and Pierre
Samuel, Commutative algebra. Vol. II, The University Series in
Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.
J.-Toronto-London-New York, 1960. MR 0120249
(22 #11006)
- [1]
- E. F. Assmus, Jr., On the homology of local rings, Illinois J. Math. 3 (1959), 18-199. MR 0103907 (21:2670)
- [2]
- M. Auslander and D. Buchsbaum, Homological dimension in local rings, Trans. Amer. Math. Soc. 85 (1957), 390-405. MR 0086822 (19:249d)
- [3]
- -, Homological dimension in Noetherian rings. II, Trans. Amer. Math. Soc. 88 (1958), 194-206. MR 0096720 (20:3203)
- [4]
- H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 446-448. MR 0157984 (28:1212)
- [5]
- -, Torsion free and projective modules, Trans. Amer. Math. Soc., to appear. MR 0140542 (25:3960)
- [6]
- H. Cartan and S. Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480 (17:1040e)
- [7]
- S. Chase, Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457-473. MR 0120260 (22:11017)
- [8]
- J. Dieudonné, Remarks on quasi-Frobenius rings, Illinois J. Math. 12 (1958), 346-354. MR 0097427 (20:3896)
- [9]
- B. Eckmann and A. Schopf, Über injective Moduln, Arch. Math. 4 (1953), 75-78. MR 0055978 (15:5d)
- [10]
- S. Eilenberg and T. Nakayama, On the dimension of modules and algebras. II, Nagoya Math. J. 9 (1955), 1-16. MR 0073577 (17:453a)
- [11]
- W. Grobner, Ein Irreduzibilitätskriterium fur Primarideale in kommutativen Ringen, Monatsh. Math. 55 (1951), 138-145. MR 0043074 (13:202b)
- [12]
- J. P. Jans, Duality of Noetherian rings, Proc. Amer. Math. Soc. 12 (1961) 829-835. MR 0137743 (25:1192)
- [13]
- E. Matlis, Injective modules over Noetherian rings, Pacific J. Math. 8 (1958), 511-528. MR 0099360 (20:5800)
- [14]
- -, Applications in duality, Proc. Amer. Math. Soc. 10 (1959), 659-662. MR 0106937 (21:5667)
- [15]
- D. G. Northcott and D. Rees, Extension and simplifications of the theory of regular local rings, J. London Math. Soc. 32 (1957), 367-374. MR 0089189 (19:630f)
- [16]
- O. Zariski and P. Samuel, Commutative algebra, Vol. II, Van Nostrand, Princeton, N. J. (1960). MR 0120249 (22:11006)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1962-0138644-8
PII:
S 0002-9947(1962)0138644-8
Article copyright:
© Copyright 1962 American Mathematical Society
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