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1999 | 81 | 2 | 237-262
Tytuł artykułu

Tame three-partite subamalgams of tiled orders of polynomial growth

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EN
Abstrakty
EN
Assume that K is an algebraically closed field. Let D be a complete discrete valuation domain with a unique maximal ideal p and residue field D/p ≌ K. We also assume that D is an algebra over the field K . We study subamalgam D-suborders $Λ^•$ (1.2) of tiled D-orders Λ (1.1). A simple criterion for a tame lattice type subamalgam D-order $Λ^•$ to be of polynomial growth is given in Theorem 1.5. Tame lattice type subamalgam D-orders $Λ^•$ of non-polynomial growth are completely described in Theorem 6.2 and Corollary 6.3.
Słowa kluczowe
Rocznik
Tom
81
Numer
2
Strony
237-262
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-02-15
Twórcy
  • Faculty of Mathematics and Informaticsi, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [1] D. M. Arnold and M. Dugas, Block rigid almost completely decomposable groups and lattices over multiple pullback rings, J. Pure Appl. Algebra 87 (1993), 105-121.
  • [2] C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. I, Wiley Classics Library Edition, New York, 1990.
  • [3] P. Dowbor and S. Kasjan, Galois covering technique and tame non-simply connected posets of polynomial growth, J. Pure Appl. Algebra 1999, in press.
  • [4] J. A. Drozd and M. G. Greuel, Tame-wild dichotomy for Cohen-Macaulay modules, Math. Ann. 294 (1992), 387-394.
  • [5] Y. A. Drozd, Cohen-Macaulay modules and vector bundles, in: Interactions between Ring Theory and Representations of Algebras (Murcia, 1998), Lecture Notes in Pure and Appl. Math., Marcel Dekker, 1999, to appear.
  • [6] P. Gabriel and A. V. Roiter, Representations of Finite Dimensional Algebras, Algebra VIII, Encyclopedia Math. Sci. 73, Springer, 1992.
  • [7] E. L. Green and I. Reiner, Integral representations and diagrams, Michigan Math. J. 25 (1978), 53-84.
  • [8] S. Kasjan, Adjustment functors and tame representation type, Comm. Algebra 22 (1994), 5587-5597.
  • [9] S. Kasjan, Minimal bipartite algebras of infinite prinjective type with prin-preprojective component, Colloq. Math. 76 (1998), 295-317.
  • [10] S. Kasjan, A criterion for polynomial growth of $\widetilde 𝔸_n$-free two-peak posets of tame prinjective type, preprint, Toruń, 1998.
  • [11] S. Kasjan and D. Simson, Tame prinjective type and Tits form of two-peak posets I, J. Pure Appl. Algebra 106 (1996), 307-330.
  • [12] S. Kasjan and D. Simson, Tame prinjective type and Tits form of two-peak posets II, J. Algebra 187 (1997), 71-96.
  • [13] S. Kasjan and D. Simson, A subbimodule reduction, a peak reduction functor and tame prinjective type, Bull. Polish Acad. Sci. Math. 45 (1997), 89-107.
  • [14] L. A. Nazarova and V. A. Roiter, Representations of completed posets, Comment. Math. Helv. 63 (1988), 498-526.
  • [15] J. A. de la Pe na and D. Simson, Prinjective modules, reflection functors, quadratic forms and Auslander-Reiten sequences, Trans. Amer. Math. Soc. 329 (1992), 733-753.
  • [16] C. M. Ringel and K. W. Roggenkamp, Diagrammatic methods in the representation theory of orders, J. Algebra 60 (1979), 11-42.
  • [17] D. Simson, A splitting theorem for multipeak path algebras, Fund. Math. 138 (1991), 113-137.
  • [18] D. Simson, Right peak algebras of two-separate stratified posets, their Galois coverings and socle projective modules, Comm. Algebra 20 (1992), 3541-3591.
  • [19] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl. 4, Gordon & Breach, New York, 1992.
  • [20] D. Simson, Posets of finite prinjective type and a class of orders, J. Pure Appl. Algebra 90 (1993), 77-103.
  • [21] D. Simson, On representation types of module subcategories and orders, Bull. Polish Acad. Sci. Math. 41 (1993), 77-93.
  • [22] D. Simson, A reduction functor, tameness and Tits form for a class of orders, J. Algebra 174 (1995), 430-452.
  • [23] D. Simson, Triangles of modules and non-polynomial growth, C. R. Acad. Sci. Paris Sér. I 321 (1995), 33-38.
  • [24] D. Simson, Representation embedding problems, categories of extensions and prinjective modules, in: Representation Theory of Algebras (Cocoyoc, 1994), CMS Conf. Proc. 18, Amer. Math. Soc., 1996, 601-639.
  • [25] D. Simson, Socle projective representations of partially ordered sets and Tits quadratic forms with application to lattices over orders, in: Abelian Groups and Modules (Colorado Springs, 1995), Lecture Notes in Pure and Appl. Math. 182, Marcel Dekker, 1996, 73-111.
  • [26] D. Simson, Prinjective modules, propartite modules, representations of bocses and lattices over orders, J. Math. Soc. Japan 49 (1997), 31-68.
  • [27] D. Simson, Representation types, Tits reduced quadratic forms and orbit problems for lattices over orders, in: Trends in the Representation Theory of Finite Dimensional Algebras (Seattle, 1997), Contemp. Math. 229, Amer. Math. Soc., 1998, 307-342.
  • [28] D. Simson, Three-partite subamalgams of tiled orders of finite lattice type, J. Pure Appl. Algebra 138 (1999), 151-184.
  • [29] D. Simson, A reduced Tits quadratic form and tameness of three-partite subamalgams of tiled orders, Trans. Amer. Math. Soc., in press.
  • [30] D. Simson, Cohen-Macaulay modules over classical orders, in: Interactions between Ring Theory and Representations of Algebras (Murcia, 1998), Lecture Notes in Pure and Appl. Math., Marcel Dekker, 1999, to appear.
  • [31] A. Skowroński, Group algebras of polynomial growth, Manuscripta Math. 59 (1987), 499-516.
  • [32] A. Skowroński, Criteria for polynomial growth of algebras, Bull. Polish Acad. Sci. Math. 42 (1994), 173-183.
  • [33] Y. Yoshino, Brauer-Thrall type theorem for maximal Cohen-Macaulay modules, J. Math. Soc. Japan 39 (1987), 719-739.
  • [34] Y. Yoshino, Cohen-Macaulay Modules over Cohen-Macaulay Rings, London Math. Soc. Lecture Note Ser. 146, Cambridge Univ. Press, 1990.
  • [35] A. G. Zavadskij and V. V. Kirichenko, Torsion-free modules over prime rings, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 57 (1976), 100-116 (in Russian).
  • [36] A. G. Zavadskij and V. V. Kirichenko, Semimaximal rings of finite type, Mat. Sb. 103 (1977), 323-345 (in Russian).
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