The existence of dual modules
HTML articles powered by AMS MathViewer
- by D. D. Anderson
- Proc. Amer. Math. Soc. 55 (1976), 258-260
- DOI: https://doi.org/10.1090/S0002-9939-1976-0399067-5
- PDF | Request permission
Abstract:
In this note we show that a Noetherian module has a dual module if and only if it satisfies $AB{5^{\ast }}$. A connection between completeness and $AB{5^{\ast }}$ is also established.References
- Reinhold Baer, Dualism in Abelian groups, Bull. Amer. Math. Soc. 43 (1937), no. 2, 121–124. MR 1563499, DOI 10.1090/S0002-9904-1937-06507-4
- Hyman Bass, Descending chains and the Krull ordinal of commutative Noetherian rings, J. Pure Appl. Algebra 1 (1971), no. 4, 347–360. MR 302634, DOI 10.1016/0022-4049(71)90002-8
- E. W. Johnson, A note on quasi-complete local rings, Colloq. Math. 21 (1970), 197–198. MR 265352, DOI 10.4064/cm-21-2-197-198
- Eben Matlis, Injective modules over Noetherian rings, Pacific J. Math. 8 (1958), 511–528. MR 99360
- Eben Matlis, Modules with descending chain condition, Trans. Amer. Math. Soc. 97 (1960), 495–508. MR 169879, DOI 10.1090/S0002-9947-1960-0169879-4
- Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856
- D. W. Sharpe and P. Vámos, Injective modules, Cambridge Tracts in Mathematics and Mathematical Physics, No. 62, Cambridge University Press, London-New York, 1972. MR 0360706
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 55 (1976), 258-260
- DOI: https://doi.org/10.1090/S0002-9939-1976-0399067-5
- MathSciNet review: 0399067