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1998 | 77 | 1 | 121-132
Tytuł artykułu

The Local Duality for Homomorphisms and an Application to Pure Semisimple PI-Rings

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
77
Numer
1
Strony
121-132
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-05-17
poprawiono
1997-11-28
Twórcy
  • Katedra Algebry, MFF-UK, Sokolovská 83, 18675 Praha 8, Czech Republic
Bibliografia
  • [1] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules 2nd ed., Grad. Texts in Math. 13, Springer, New York, 1992.
  • [2] M. Auslander, Representation theory of artin algebras I Comm. Algebra 1 (1974), 177-268.
  • [3] M. Auslander, Large modules over artin algebras in: Algebra, Topology and Category Theory, Academic Press, New York, 1976, 1-17.
  • [4] M. Auslander, Functors and morphisms determined by objects in: Representation Theory of Algebras, Lecture Notes in Pure Appl. Math. 37, Dekker, New York, 1978, 1-244.
  • [5] M. Auslander, Applications of morphisms determined by modules ibid., 245-327.
  • [6] M. Auslander and I. Reiten, On the representation type of triangular matrix rings J. London Math. Soc. (2) 12 (1976), 371-382.
  • [7] M. Auslander, I. Reiten and S. O. Smalο, Representation Theory of Artin Algebras Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, Cambridge, 1995.
  • [8] J.-E. Björk, Rings satisfying a minimum condition on principal ideals J. Reine Angew. Math. 236 (1969), 112-119.
  • [9] P. M. Cohn, Algebra 2 2nd ed., Wiley, Chichester, 1989.
  • [10] I. Herzog, A test for finite representation type J. Pure Appl. Algebra 95 (1994), 151-182.
  • [11] C. U. Jensen and H. Lenzing, Model-Theoretic Algebra with Particular Emphasis on Fields, Rings, Modules Algebra Logic Appl. 2, Gordon and Breach, New York, 1989.
  • [12] H. Krause, Dualizing rings and a characterisation of finite representation type C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), 507-510.
  • [13] M. Prest, Model Theory and Modules London Math. Soc. Lecture Note Ser. 130, Cambridge Univ. Press, Cambridge, 1988.
  • [14] C. M. Ringel and H. Tachikawa, QF-3 rings J. Reine Angew. Math. 272 (1975), 49-72.
  • [15] A. Rosenberg and D. Zelinsky, Finiteness of the injective hull Math. Z. 70 (1959), 372-380.
  • [16] M. Schmidmeier, Auslander-Reiten Köcher für artinsche Ringe mit Polynomidentität Dissertation Univ. München, 1996, 88 pp.
  • [17] M. Schmidmeier, A dichotomy for finite length modules induced by local duality Comm. Algebra 25 (1997), 1933-1944.
  • [18] M. Schmidmeier, Auslander-Reiten theory for artinian PI-rings J. Algebra, to appear.
  • [19] M. Schmidmeier, Endofinite modules over hereditary artinian PI-rings in: Proc. Conf. ICRA VIII, to appear.
  • [20] D. Simson, Functor categories in which every flat object is projective Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 22 (1974), 375-380.
  • [21] D. Simson, Partial Coxeter functors and right pure semisimple hereditary rings J. Algebra 71 (1981), 195-218.
  • [22] D. Simson, Indecomposable modules over one-sided serial local rings and right pure semisimple rings Tsukuba J. Math. 7 (1983), 87-103.
  • [23] D. Simson, On right pure semisimple hereditary rings and an Artin problem J. Pure Appl. Algebra 104 (1995), 313-332.
  • [24] D. Simson, An Artin problem for division ring extensions and the pure semisimplicity conjecture I Arch. Math. (Basel) 66 (1996), 114-122.
  • [25] D. Simson, A class of potential counter-examples to the pure semisimplicity conjecture in: Proc. Conf. Algebra and Model Theory, Essen-Dresden, 1994 and 1995, Gordon and Breach, London, 1997, 345-373.
  • [26] B. Zimmermann-Huisgen and W. Zimmermann, On the sparsity of representations of rings of pure global dimension zero Trans. Amer. Math. Soc. 320 (1990), 695-711.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv77z1p121bwm
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