Cohen-Macaulay and Gorenstein finitely graded rings

Claudia Menini

Rendiconti del Seminario Matematico della Università di Padova (1988)

  • Volume: 79, page 123-152
  • ISSN: 0041-8994

How to cite

top

Menini, Claudia. "Cohen-Macaulay and Gorenstein finitely graded rings." Rendiconti del Seminario Matematico della Università di Padova 79 (1988): 123-152. <http://eudml.org/doc/108089>.

@article{Menini1988,
author = {Menini, Claudia},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Cohen-Macaulay graded rings; Gorenstein graded rings; semitrivial extensions},
language = {eng},
pages = {123-152},
publisher = {Seminario Matematico of the University of Padua},
title = {Cohen-Macaulay and Gorenstein finitely graded rings},
url = {http://eudml.org/doc/108089},
volume = {79},
year = {1988},
}

TY - JOUR
AU - Menini, Claudia
TI - Cohen-Macaulay and Gorenstein finitely graded rings
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1988
PB - Seminario Matematico of the University of Padua
VL - 79
SP - 123
EP - 152
LA - eng
KW - Cohen-Macaulay graded rings; Gorenstein graded rings; semitrivial extensions
UR - http://eudml.org/doc/108089
ER -

References

top
  1. [AM] M.F. Atiyah - I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, London, 1969. Zbl0175.03601MR242802
  2. [B] H. Bass, On the ubiquity of Gorenstein rings, Math. Zeitschr., 82 (1963) pp. 8-28. Zbl0112.26604MR153708
  3. [BG] M. Boratynski - S. Greco, When does an ideal arise from the Ferrand construction?, Rapporto interno del Dipartimento di Matematica del Politecnico di Torino N. 2, (1985). Zbl0621.13001
  4. [F1] D. Ferrand, Courbes gauches et fibrés de rang 2, C.R. Acad. Sci. Paris, 281 (1975), pp. 345-347. Zbl0315.14019MR379517
  5. [F2] R. Fossum, Commutative extensions by canonical modules are Gorenstein rings, PAMS, 40 (1973), pp. 395-400. Zbl0271.13013MR318139
  6. [FGR] R.M. Fossum - P.A. Griffith - I. Reiten, Trivial Extensions of Abelian Categories, LNM456, Springer-Verlag, Berlin-Heidelberg-New York, 1975. Zbl0303.18006MR389981
  7. [H] R. Hartshorne, Local Cohomology, LNM 41, Springer-Verlag, Berlin-Heidelberg -New York, 1967. MR224620
  8. [HK] J. Herzog - E. Kunz, Der Kanonische Modul eines Cohen-Macaulay Rings, LNM238, Springer-Verlag, Berlin-Heidelberg-New York, 1973. Zbl0231.13009MR412177
  9. [K] I. Kaplansky, Commutative rings, The University of Chicago Press, Chicago and London, 1974. Zbl0296.13001MR345945
  10. [M1] E. Matlis, Injective modules over Noetherian rings, Pacific J. Math., 8 (1958), pp. 511-528. Zbl0084.26601MR99360
  11. [M2] E. Matlis, The Higher Properties of R-Sequences, J. of Algebra, 50 (1978), pp. 77-112. Zbl0384.13002MR479882
  12. [M 3] H. Matsumura, Commutative Algebra, Benjamin, New York, 1970. Zbl0211.06501MR266911
  13. [M4] C. Menini, Finitely graded rings, Morita duality and self-injectivity, Comm. in Algebra, 15 (1987), pp. 1357-1364. Zbl0618.18004MR898292
  14. [N] C Năstăsescu, Strongly graded rings of finite groups, Comm. in Algebra, 11 (1983), pp. 1033-1071. Zbl0522.16002MR700723
  15. [NV] C Năstăsescu - F. Van Oystaeyen, Graded Ring Theory, North-Holland, Amsterdam-New York-Oxford, 1982. Zbl0494.16001MR676974
  16. [R] I. Reiten, The converse to a theorem of Sharp on Gorenstein modules, Proc. of A.M.S., 32 (1970), pp. 417-420. Zbl0235.13016MR296067
  17. [S 1] J.P. Serre, Algebre Locale. Multiplicités, LNM11, Springer-Verlag, Berlin-Heidelberg- New York, 1965. Zbl0142.28603MR201468
  18. [S2] R.Y. Sharp, Local Cohomology Theory in Commutative Algebra, Quart. J. Math. Oxford (2), 21 (1970), pp. 425-434. Zbl0204.06003MR276217
  19. [S3] R.Y. Sharp, Gorenstein Modules, Math. Z., 115 (1970), pp. 117-139. Zbl0186.07403MR263801

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.