Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Injective dimension in Noetherian rings


Author: Hyman Bass
Journal: Trans. Amer. Math. Soc. 102 (1962), 18-29
MSC: Primary 16.25; Secondary 16.20
DOI: https://doi.org/10.1090/S0002-9947-1962-0138644-8
MathSciNet review: 0138644
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [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)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16.25, 16.20

Retrieve articles in all journals with MSC: 16.25, 16.20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1962-0138644-8
Article copyright: © Copyright 1962 American Mathematical Society

American Mathematical Society