Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Cover of the book
Tytuł książki

Moduled categories and adjusted modules over traced rings

Seria
Rozprawy Matematyczne tom/nr w serii: 269 wydano: 1990
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
1. Introduction.......................................................................................5
2. Traced rings and adjusted modules..................................................9
3. Moduled categories.........................................................................21
4. Triangular adjustments....................................................................32
5. Categories of matrices and $_{A}M_{B}$-matrix modules...............43
6. Trace and cotrace reductions.........................................................47
7. Concluding remarks........................................................................60
References.........................................................................................64
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 269
Liczba stron
67
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLXIX
Daty
wydano
1990
Twórcy
  • Instytut Matematyki Uniwersytetu Mikołaja Kopernika , Chopina 12-18, 87 100 Toruń, Polska
  • Institute of Mathematics, Nicholas Copernicus University, Chopina 12-18, 87 100 Toruń, Poland
Bibliografia
  • [1] F. W. Anderson and K. R. Fuller, Rings and categories of modules. Graduate Texts in Mathematics, Vol. 13, Springer Verlag, New York-Heidelberg-Berlin 1973.
  • [2] M. Auslander, Representation theory of Artin algebras, I, Comm. Algebra 1 (1974), 177 268.
  • [3] M. Auslander, Representation theory of Artin algebras, II, ibid. 1 (1974), 269-310.
  • [4] M. Auslander, Large modules over Artin algebras, in. Algebra, Topology and Category Theory, Academic Press, New York, 1976, 3-17.
  • [5] M. Auslander, Functors and morphisms determined by objects, Proc. Conf. on Representation Theory (Philadelphia 1976), Marcel Dekker, 1978, 1-244.
  • [6] M. Auslander, Applications of morphisms determined by objects. Proc. Conf. on Representation Theory (Philadelphia 1976), Marcel Dekker, 1978, 245-327.
  • [7] M. Auslander and I. Reiten, Stable equivalence of Artin algebras, Proc. Conf. on Orders, Group Rings and Related Topics, Lecture Notes in Math. 353 (1973), 8-71.
  • [8] M. Auslander, Representation theory of Artin algebras, III, Comm. Algebra 3 (1975), 239-294.
  • [9] M. Auslander and I. Reiten, On the representation type of triangular matrix rings, J. London Math. Soc. 12 (1976), 371-382.
  • [10] M. Auslander, M. I. Platzek and I. Reiten, Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 (1979), 1-16.
  • [11] M. Auslander and S. O. Smalø, Almost split sequences in subcategories, J. Algebra 69 (1981), 426-454.
  • [12] R. Bautista, Torsion theories and Auslander-Reiten sequences, An. Inst. Mat. Nac. Autónoma México, 19 (1979), 1-19.
  • [13] R. Bautista and D. Simson, Torsionless modules over L-hereditary 1-Gorenstein artinian rings, Comm. Algebra 12 (1984), 899-936.
  • [14] I. N. Bernstein, I. M. Gelfand and V. A. Ponomarev, Coxeter functors and Gabriel's theorem, Uspekhi Mat. Nauk 28 (1973), 19-33.
  • [15] K. Bongartz and P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (1982), 331-378.
  • [16] E. Dieterich, Classification of the indecomposable representations of the cyclic group of order three in a complete discrete valuation ring of ramification degree four, Talk at the Fourth International Conference on Representations on Algebras, Carleton University, Ottawa, August 1984.
  • [17] V. Dlab and C. M. Ringel, On algebras ofi finite representation type, J. Algebra 33 (1975), 306-394.
  • [18] V. Dlab and C. M. Ringel, Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. 173 (1976).
  • [19] P. Dowbor, C. M. Ringel and D. Simson, Hereditary artinian rings of finite representation type, in: Representation Theory II, Lecture Notes in Math. 832 (1980), 232-241.
  • [20] P. Dowbor and A. Skowroński, Galois coverings of representation-infinite algebras, Comment. Math. Helv. 62 (1987), 311 -337.
  • [21] P. Dowbor and D. Simson, Quasi-Artin species and rings of finite representation type, J. Algebra 63 (1980), 435-143.
  • [22] Ju. A. Drozd, Coxeter transformations and representations of partially ordered sets, Funktsional. Anal, i Prilozhen., 8 (1974), 34-42.
  • [23] P. Dowbor, Matrix problems and categories of matrices, Zap. Nauchn. Sem. LOMI 28 (1972), 144-153.
  • [24] K. R. Fuller, On rings whose left modules are direct sums of finitely generated modules. Proc. Amer. Math. Soc. 54 (1976), 39-14.
  • [25] K. R. Fuller and H. Hullinger, Rings with finiteness conditions and their categories of functors, J. Algebra 55 (1978), 94-105.
  • [26] P. Gabriel, Des catégories abéliennes. Bull. Soc. Math. France 90 (1962), 323-48.
  • [27] P. Gabriel, Unzerlegbare Darstellungen I, Manuscripta Math., 6 (1972), 71-103.
  • [28] P. Gabriel, Indecomposable representations II, in: Symposia Mathematica Vol. XI, Academic Press, London, 1973, 81-104.
  • [29] P. Gabriel, The universal covering of a representation-finite algebra, Lecture Notes in Math. 903, Springer, New York, 1981, 66-105.
  • [30] E. L. Green and I. Reiner, Integral representations and diagrams, Michigan Math. J. 25 (1978), 53-84.
  • [31] L. Gruson and C. U. Jensen, Dimensions cohomologiques reliées aux foncteurs $lim_{←}^(i)$ Lecture Notes in Math. 867, Springer, Berlin, 1981.
  • [32] M. Harada, Factor categories with applications to direct decomposition of modules, Lecture Notes in Pure and Appl. Math. 88, Marcel Dekker, Inc., New York and Basel, 1984.
  • [33] M. Kleiner, Partially ordered sets of finite type. Zap. Nauchn. Sem. LOMI, 28 (1972), 32-41.
  • [34] B. Klemp and D. Simson, A diagrammatic characterization of schurian vector space PI-categories of finite type, Bull. Polish Acad. Sci. Math. 32 (1984), 11-18.
  • [35] B. Klemp and D. Simson, Schurian sp-representation-finite right peak PI-rings and their indecomposable socle projective modules, J. Algebra (1990), in print.
  • [36] N. Marmaridis, Generalized vector space categories, Abstracts of the Fourth International Conference on Representations of Algebras, Carleton University, Ottawa, August 1984.
  • [37] H. Meitzer and A. Skowroński, Group algebras of finite representation type, Math, Z. 182 (1983), 129-148.
  • [38] K. Morita, Localizations in categories of modules, I, ibid. 114 (1970), 121-144.
  • [39] K. Nishida, Representations of orders and vector space categories, J. Pure Appl. Algebra 33 (1984} 209-217.
  • [40] L. A. Nazarova, Representations of partially ordered sets of infinite type, Izv. Akad. Nauk SSSR, Ser. Mat. 39 (1975), 963-991.
  • [41] L. A. Nazarova and A. V. Rojter, Representations of partially ordered sets, Zap. Nauchn. Sem. LOMI 28 (1972), 5-31.
  • [42] L. A. Nazarova and A. V. Rojter, Kategorielle Matrizen-Probleme und die Brauer-Thrall-Vermutung, Mitt. Math. Sem. Giessen 115 (1975), 1-153.
  • [43] L. A. Nazarova and A. V. Rojter, Representations and form of weakly completed partially ordered sets, in: Linear Algebra and Representation Theory, Akad. Nauk Ukrainskoj SSR, Institute of Mathematics, Kiev, 1983, 19-54.
  • [44] C. M. Ringel, Report on the Brauer-Thrall conjecture, in: Representation Theory I, Lecture Notes in Math. 831 (1980), 104-136.
  • [45] C. M. Ringel, Tame algebras, ibid., 137 -287.
  • [46] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099 (1984).
  • [47] C. M. Ringel and K. W. Roggenkamp, Diagrammatic methods in the representation theory of orders, J. Algebra 60 (1979), 11-42.
  • [48] C. M. Ringel, Socle-determined categories of representations of artinian hereditary tensor algebras, ibid. 64 (1980), 249-269.
  • [49] A. V. Rojter, Matrix problems and representations of bisystems, Zap. Nauchn. Sem. LOMI 28 (1972), 130- 143.
  • [50] K. W. Roggenkamp and A. Wiedemann, Auslander-Reiten quivers and Schurian orders, Comm. Algebra 12 (1984), 2525-2578.
  • [51] A. Rosenberg and D. Zelinsky, Finiteness of the injective hull. Math. Z. 70 (1959), 372-380.
  • [52] W. Rump, Existence and uniqueness of representation coverings for completely reducible orders, in Proc. of the Fourth International Conference of Representations of Algebras, Carleton University, Ottawa, 1984.
  • [53] D. Simson, Functor categories in which every flat object is projective, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys. 22 (1974), 375-380.
  • [54] D. Simson, Pure semisimple categories and rings of finite representation type, J. Algebra 48 (1977), 290-296.
  • [55] D. Simson, Partial Coxeter functors and right pure semisimple hereditary rings, ibid. 71 (1981), 195-218.
  • [56] D. Simson, Indecomposable modules over one-sided serial rings and right pure semisimple rings, Tsukuba J. Math. 7 (1983), 87-103.
  • [57] D. Simson, Representations of Partially Ordered Sets, Vector Space Categories and Socle Projective Module, Paderborn, July 1983, 1-141.
  • [58] D. Simson, Special schurian vector space categories and l-hereditary right QF-2 artinian rings, Comment. Math. 25 (1984), 137-149.
  • [59] D. Simson, Right pure semisimple l-hereditary PI-rings, Rend. Sem. Mat. Univ. Padova 71 (1984), 141-175.
  • [60] D. Simson, Vector space categories, right peak rings and their socle projective modules, J. Algebra 92 (1985), 532-571.
  • [61] D. Simson, On vector space categories and differentiations of right peak rings, in Proc. of the Fourth International Conference on Representations of Algebras, Carleton University, Ottawa, August 1984.
  • [62] D. Simson, Socle reductions and socle projective modules, J. Algebra, 103 (1986), 18-68.
  • [63] D. Simson, Peak reductions and waist reflection functors, to appear in Fund. Math. 137 (1991).
  • [64] D. Simson, On differentiation procedures for right peak rings and socle projective modules. Bull. Polish Acad. Sci. Math. 35 (1987), 279-288.
  • [65] D. Simson, A narrow over-ring adjustment functor, to appear in J. Algebra 1990.
  • [66] D. Simson and A. Skowroński, Extensions of artinian rings by hereditary injective modules, in: Representations of Algebras, Lecture Notes in Math. 903, Springer, London, 1981, 315-330.
  • [67] A. Skowroński, On triangular matrix rings of finite representation type. Bull. Polish Acad. Sci. Math. 31 (1983), 227-233.
  • [68] H. Tachikawa, Quasi-Frobenius Rings and Generalizations, Lecture Notes in Math. 351, Springer, Berlin, 1973.
  • [69] P. Vamos, Semilocal noetherian PI-rings, Bull. London Math. Soc. 9 (1977), 251-256.
  • [70] A. G. Zavadskii and V. V. Kirichenko, Torsion-free modules over primary rings, Zap. Nauchn. Sem. LOMI 57 (1976) 100-116.
  • [71] A. G. Zavadskii and V. V. Kirichenko, Semimaximal rings of finite type, Mat. Sb. 103 (1977), 323-345.
  • [72] J. Waschbüsch, Über Bimoduln in Artinringen vom endlich Modultyp, Comm. Algebra 8 (1980), 105-151.
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-beeebe4f-0ea0-4ebe-a969-0d5f77bcb5ac
Identyfikatory
ISBN
83-01-09341-2
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

rozwiń roczniki

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.