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On the ubiquity of Gorenstein rings

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References

  1. Auslander, M., andO. Goldman: Maximal orders. Trans. Amer. Math. Soc.97, 1–24 (1960).

    Google Scholar 

  2. Bass, H.: Finitistic dimension and a homological generalization of semi-primary rings. Trans. Amer. Math. Soc.95, 466–488 (1960).

    Google Scholar 

  3. —: Injective dimension in noetherian rings. Trans. Amer. Math. Soc.102, 18–29 (1962).

    Google Scholar 

  4. —: Torsion free and projective modules. Trans. Amer. Math. Soc.102, 319–327 (1962).

    Google Scholar 

  5. Berger, R.: Über eine Klasse unvergabelter lokaler Ringe. Math. Ann.166, 98–102 (1962).

    Google Scholar 

  6. Dade, E. C.: Some indecomposable group representations. Ann. of Math. (to appear).

  7. Dieudonne, J.: Remarks on quasi-Frobenius rings. Ill. J. Math12, 346–354 (1958).

    Google Scholar 

  8. Gabriel, P.: Objects injectifs dans les catégories abéliennes. Sém. Dubreil 1958/59.

  9. Gorenstein, D.: An arithmetic theory of adjoint plane curves. Trans. Amer. Math. Soc.72, 414–436 (1952).

    Google Scholar 

  10. Grothendieck, A.: Théorèmes de dualité pour les faisceaux algébriques cohérents. Séminaire Bourbaki, May 1957.

  11. Heller, A., andI. Reiner: Representations of cyclic groups in rings of integers. Ann. of Math. (to appear).

  12. Jans, J.: Duality in noetherian rings. Proc. Amer. Math. Soc.12, 829–835 (1961).

    Google Scholar 

  13. Jans, J.: On finitely generated modules over noetherian rings. Trans. Amer. Math. Soc. (to appear).

  14. Kaplansky, I.: Homological dimension of rings and modules, mimeographed notes. Univ. of Chicago.

  15. Matlis, E.: Injective modules over noetherian rings. Pacific J. Math.8, 511–528 (1958).

    Google Scholar 

  16. —: Observations on noetherian domains of dimension 1. Can. J. Math.13, 569–586 (1961).

    Google Scholar 

  17. Northcott, D. G., andD. Rees: Principal systems. Quart. J. Math.8, 119–127 (1957).

    Google Scholar 

  18. Rees, D.: The grade of an ideal or module. Proc. Camb. Phil. Soc.53, 28–42 (1957).

    Google Scholar 

  19. Roquette, P.: Über den Singularitätsgrad von Teilringen in Funktionenkörpern. Math. Z.77, 228–240 (1961).

    Google Scholar 

  20. Samuel, P.: Singularités des variétés algébriques. Bull. Soc. Math. de France79, 121–129 (1951).

    Google Scholar 

  21. Serre, J.-P.: Groupes algébriques et corps de classes. Paris: Hermann 1959.

    Google Scholar 

  22. Serre, J.-P.: Sur les modules projectifs. Séminaire Dubreil, Nov. 1960/61.

  23. Apéry, R.: La géométrie algébrique. Bull. Soc. Math. France71, 46–66 (1943).

    Google Scholar 

  24. Rosenlicht, M.: Equivalence relations on algebraic curves. Ann. of Math.56, 169–191 (1952).

    Google Scholar 

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Bass, H. On the ubiquity of Gorenstein rings. Math Z 82, 8–28 (1963). https://doi.org/10.1007/BF01112819

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