On graded rings, I

Journal of the Mathematical Society of Japan

Volumn 30, Issue 2, 1978, Pages 181-213

  Goto, Shiro ^a   Watanabe, Keiichi ^b  

^a NIHON UNIVERSITY   (Japan)

^b TOKYO METROPOLITAN UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84972561298     PISSN: 00255645     EISSN: 18811167     Source Type: Journal    
DOI: 10.2969/jmsj/03020179     Document Type: Article

References (37)

1. Altman-Kleiman, An introduction to Grothendieck duality theory, Springer Lecture Notes, 146 (1970).
2. H. Bass, On the ubiquity of Gorenstein rings, Math. Z., 82 (1963), 8-28.
3. Bourbaki, Algebre Commutative, Chapter III, IV.
4. Cartan-Eilenberg, Homological Algebra, Princeton Univ. Press, 1956.
5. W.-L. Chow, On unmixedness therem, Amer. J. Math., 86 (1964), 799-822.
6. P. Gabriel, Des categories abeliennes, Bull. Soc. Math. France, 90 (1962), 323-448.
7. S. Goto, Veronesean subrings of Gorenstein rings, J. Math. Kyoto Univ., 16 (1976), 51-55.
8. Grothendieck, E. G. A. Chapter II, Publ. I. H. E. S., 8.
9. Grothendieck, E. G. A. Chapter III, Publ. I. H. E. S., 11.
10. Grothendieck, E. G.A. Chapter IV, Publ. I.H. E. S., 24.
11. Grothendieck, Local cohomology, Springer Lecture Notes, 41 (1967).
12. R. Hartshorne, Residues and duality, Springer Lecture Notes, 20 (1966).
13. R. Hartshorne, Affine duality and cofiniteness, Invent. Math., 9 (1970), 145-164.
14. J. Herzog and E. Kunz, Die Werthalbgruppe eines lokalen Rings der Dimension 1, Ber. Heidelberger Akad. Wiss., 1971.
15. J. Herzog and E. Kunz, Der kanonische Modul eines Cohen-Macaulay Rings, Springer Lecture Notes, 238 (1971).
16. M. Hochster and J.A. Eagon, Cohen-Macaulay rings, invariant theory and the generic perfection of determinantal loci, Amer. J. Math., 93 (1971), 1020-1058.
17. M. Hochster and J. L. Roberts, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Advances in Math., 13 (1974), 115-175.
18. F. S. Macaulay, The Algebraic Theory of Modular Systems, Cambridge Tracts, 1916.
19. J. Matijevic and P. Roberts, A conjecture of Nagata on graded Cohen-Macaulay rings, J. Math. Kyoto Univ., 14 (1974), 125-128.
20. E. Matlis, Injective modules over Noetherian rings, Pacific J. Math., 8 (1958), 511-528.
21. T. Matsuoka, On an invariant of Veronesean rings, Proc. Japan Acad., 50 (1974), 287-291.
22. R. Shafarevich, Algebraic Surfaces, Moskva, 1965.
23. R. Y. Sharp, The Cousin complex for a module over a commutative Noetherian ring, Math. Z., 112 (1969), 340-356.
24. R. Y. Sharp, Gorenstein modules, Math. Z., 115 (1970), 117-139.
25. R. Y. Sharp, On Gorenstein modules over a complete Cohen-Macaulay local ring, Quart. J. Math. Oxford, 22 (1971), 425-434.
26. P. Wagreich, Singularities of complex surfaces with solvable local fundamental groups, Topology, 11 (1972), 51-72.
27. K. Watanabe, Some examples of one dimensional Gorenstein domains, Nagoya Math. J., 49 (1973), 101-109.
28. K. Watanabe, Certain invariant subrings are Gorenstein, I and II, Osaka J. Math., 11 (1974), 1-8, 379-388.
29. H. Yamada, On Macaulay’s inverse system (in Japanese), unpublished.
30. R. Gunning, Lectures on Riemann Surfaces, Princeton, 1966.
31. K. Saito, Einfach-elliptishe Singularitaten, Invent. Math., 23 (1974), 289-325.
32. Y. Aoyama and S. Goto, On the type of graded Cohen-Macaulay rings, J. Math. Kyoto Univ., 15 (1975), 19-23.
33. J. Matijevic, Three local conditions on a graded ring, Trans. Amer. Math. Soc., 205 (1975), 275-284.
34. M. Sakaguchi, A note on Graded Gorenstein Modules, Hiroshima Math. J., 4 (1974), 339-341.
35. R. Fossum and H.-B. Foxby, The category of graded modules, Math. Scand., 35 (1974), 288-300
36. R. Fossum, The structure of indecomposable injective modules, Math. Scand., 36 (1975), 291-312.
37. S. Maclane, Homology, Springer, Berlin, 1963.