Skip to main content

When is the double Yoneda ext-algebra of a local noetherian ring again noetherian?

  • Conference paper
  • First Online:
Algebra, Algebraic Topology and their Interactions

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1183))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. ANICK, D.J., A counterexample to a conjecture of Serre, Ann. Math., 115, 1982, 1–33. Correction: Ann. Math., 116, 1983, 661.

    Article  MathSciNet  MATH  Google Scholar 

  2. ANICK, D.J., Connections between Yoneda and Pontrjagin algebras, Lecture Notes in Mathematics, 1051, 1984, 331–350, Springer-Verlag, Berlin, Heidelberg, New York and Tokyo.

    MATH  Google Scholar 

  3. ATIYAH, M.F. and MACDONALD, I.G. Introduction to Commutative Algebra, Addison-Wesley, Reading, Mass., 1969.

    MATH  Google Scholar 

  4. AVRAMOV, L., Local algebra and rational homotopy, Astérisque, 113–114, 1984, 15–43.

    MathSciNet  MATH  Google Scholar 

  5. AVRAMOV, L., Differential graded models for local rings, RIMS Kokyuroku, 446, 1981, 80–88, Kyoto Research Institute for Mathematical Sciences, Kyoto, Japan.

    MATH  Google Scholar 

  6. BACKELIN, J., Les anneaux locaux à relations monomiales ont des séries de Poincaré-Betti rationnelles, Comptes rendus Acad. Sc. Paris, 295, Série I, 1982, 607–610.

    MathSciNet  MATH  Google Scholar 

  7. BØGVAD,R. and HALPERIN, S., On a conjecture of Roos, These Proceedings.

    Google Scholar 

  8. CARTAN, H. and EILENBERG, S., Homological Algebra, Princeton Univ. Press, Princeton, 1956.

    MATH  Google Scholar 

  9. COHEN, F.R., MOORE, J.C. and NEISENDORFER, J.A., Torsion in homotopy groups, Ann. Math., 109, 1979, 121–168.

    Article  MathSciNet  MATH  Google Scholar 

  10. FRÖBERG, R., A study of graded extremal rings and of monomial rings, Math. Scand., 51, 1982, 22–34.

    MathSciNet  MATH  Google Scholar 

  11. GOVOROV, V.E., Dimension and multiplicity of graded algebras, Siberian Math. J., 14, 1973, 840–845.

    Article  MathSciNet  MATH  Google Scholar 

  12. GULLIKSEN, T.H., A change of ring theorem with applications to Poincaré series and intersection multiplicity, Math. Scand. 34, 1974, 167–183.

    MathSciNet  MATH  Google Scholar 

  13. GULLIKSEN, T.H. and LEVIN, G., Homology of local rings, Queen's Papers in Pure Appl. Math., no 20, Queen's Univ., Kingston, Ontario, 1969.

    MATH  Google Scholar 

  14. JACOBSSON, C., Finitely presented graded Lie algebras and homomorphisms of local rings, J. Pure Appl. Algebra, 38, 1985, 243–253.

    Article  MathSciNet  MATH  Google Scholar 

  15. LEMAIRE, J.-M., Algèbres connexes et homologie des espaces de lacets, Lecture Notes in Mathematics, 422, 1974, Springer-Verlag, Berlin, Heidelberg, New York.

    MATH  Google Scholar 

  16. LESCOT, Thèse, Caen 1985 and letter from J. LESCOT to J.-E. ROOS, June 14, 1985.

    Google Scholar 

  17. LEVIN, G., Large homomorphisms of local rings, Math. Scand., 46, 1980, 209–215.

    MathSciNet  MATH  Google Scholar 

  18. LEVIN, G., Finitely generated Ext algebras, Math. Scand., 49, 1981, 161–180.

    MathSciNet  MATH  Google Scholar 

  19. MACLANE, S., Homology, Springer-Verlag, Berlin, Heidelberg, New York, 1963.

    Book  MATH  Google Scholar 

  20. MILNOR, J. and MOORE, J., On the structure of Hopf algebras, Ann. Math., 81, 1965 211–264.

    Article  MathSciNet  MATH  Google Scholar 

  21. MING, R., Yoneda Products in the Cartan-Eilenberg change of rings spectral sequence with applications to BP*(BO(n)), Trans. Amer. Math. Soc., 219, 1976, 235–252.

    MathSciNet  MATH  Google Scholar 

  22. MOORE, J.C. and SMITH, L, Hopf algebras and multiplicative fibrations I-II, Amer. J. Math., 90, 1968, 752–780 and 1113–1150.

    Article  MathSciNet  MATH  Google Scholar 

  23. ROOS, J.-E., Sur l'algèbre Ext de Yoneda d'un anneau local de Golod, Comptes rendus Acad. Sc. Paris, 286, série A, 1978, 9–12.

    MATH  Google Scholar 

  24. ROOS, J.-E., Relations between the Poincaré-Betti series of loop spaces and local rings, Lecture Notes in Mathematics, 740, 1979, 285–322, Springer-Verlag, Berlin, Heidelberg, New York.

    Google Scholar 

  25. ROOS, J.-E., On the use of graded Lie algebras in the theory of local rings, London Math. Soc. Lecture Notes Series, 72, 1982, 204–230, Cambridge University Press, Cambridge.

    Google Scholar 

  26. Séminaire H. CARTAN, 11e année 1958/59, Invariant de Hopf et opérations cohomologiques sécondaires, Paris, Secr. Math., 11 rue Pierre Curie, Paris 5, 1959. (Has also been published by Benjamin, New York.)

    Google Scholar 

  27. SJÖDIN, G., A set of generators for ExtR(k,k), Math. Scand. 38, 1976, 1–12.

    Google Scholar 

  28. STANLEY, R.P., Combinatorics and Commutative Algebra, Progress in Mathematics, vol. 41, 1983, Birkhäuser, Boston, Basel, Stuttgart.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jan-Erik Roos

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Backelin, J., Roos, JE. (1986). When is the double Yoneda ext-algebra of a local noetherian ring again noetherian?. In: Roos, JE. (eds) Algebra, Algebraic Topology and their Interactions. Lecture Notes in Mathematics, vol 1183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075452

Download citation

  • DOI: https://doi.org/10.1007/BFb0075452

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16453-1

  • Online ISBN: 978-3-540-39790-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics