27
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Discrete posets, cell complexes, and the global dimension of tiled orders

Pages 55-107 | Received 01 Jan 1994, Published online: 27 Jun 2007

References

  • Ajtai , M. 1973 . On a class of finite lattices . Periodica Math. Hung , 4 : 217 – 220 .
  • Anderson , F.W. and Fuller , K.R. 1974 . Rings and categories of modules New York
  • Auslander , M. and Roggenkamp , K.W. 1972 . A characterization of orders of finite lattice type . Invent, math , 17 : 79 – 84 .
  • Bourbaki , N. 1972 . Commutative algebra Paris
  • Drozd , Ju.A and Kiriĉenko , V.V. 1972 . On quasi-Bass orders . Izv. Akad. Nauk. SSSR, Ser. Mat , 36 ( 1972 ) : 328 – 370 . = Math. USSR Izv. 6 , 323 -366
  • Fujita , H. 1990 . Tiled orders of finite global dimension . Trans. AMS , 322 ( 1972 ) : 329 – 342 .
  • Gabriel , P. 1972 . Représentations indécomposables des ensembles ordonnés , 301 – 304 . Paris : Sem. P. Dubreil . 1973
  • Grätzer , G. 1971 . “ Lattice theory ” . In First concepts and distributive lattices , Freeman .
  • Jategaonkar , V.A. Global dimension of triangular orders over a discrete valuation ring . Proc. AMS . Vol. 38 , pp. 8 – 14 .
  • Jategaonkar , V.A. 1974 . Global dimension of tiled orders over commutative noetherian domains . Trans AMS , 90 : 357 – 374 .
  • Jategaonkar , V.A. 1974 . Global dimension of tiled orders over a discrete valuation ring . Trans. AMS , 196 : 313 – 330 .
  • Jónsson , B. Distributive sublattices of a modular lattice . Proc. AMS . Vol. 6 , pp. 682 – 688 .
  • Kaplansky , I. 1972 . Fields and rings Chicago
  • Kelly , D. and Rival , I. 1974 . Crowns, fences, and dismantlable lattices . Can. J. Math , 26 : 1257 – 1271 .
  • Kirkman , E. and Kuzmanovich , J. 1989 . Global dimension of a class of tiled orders . J. Alg , 127 : 57 – 72 .
  • Mitschke , A. and Wille , R. 1976 . Finite distributive lattices projective in the class of all modular lattices . Alg. univ , 6 : 383 – 393 .
  • Nazarova , L.A. and Ro[lcirc]ter , A.V. 1972 . Representations of partially ordered sets . Zap. Naucn. Sem. LOMI , 28 ( 1975 ) : 5 – 31 . = J. Soviet Math. 23 , 585 - 607
  • Plesken , W. 1983 . Group rings of finite groups over p-adic integers , Vol. 1026 , Berlin, New York : Springer Lecture Notes in Math . Heidelberg - Tokyo
  • Ramsey , F.P. 1930 . On a problem of formal logic . Proc. LMS . 1930 . Vol. 30 , pp. 264 – 286 .
  • Reiner , I. 1975 . Maximal orders London New York - San Francisco
  • Roggenkamp , K.W. 1984 . A. Wiedemann, Auslander-Reiten quivers of Schu-rian orders . Comm. in Alg , 12 : 2525 – 2578 .
  • Rump , W. 1986 . Enlacements and representation theory of completely reducible orders . Spinger Lecture Notes in math , 1178 : 272 – 308 . Berlin - Heidelberg
  • Rump , W. 1990 . Irreduzible und unzerlegbare Darstellungen klassischer Ordnungen . Bayreuther Math. Sehr , 32 : 1 – 405 .
  • Tarsy , R.B. 1970 . Global dimension of orders . Trans. AMS , 151 : 335 – 340 .
  • Tutte , W.T. 1956 . A class of abelian groups . Can. J. Math , 8 : 13 – 28 .
  • Tutte , W.T. 1958 . A homotopy theorem for matroids I, II . Trans. AMS , 88 : 144 – 174 .
  • Tutte , W.T. 1959 . Matroïds and graphs . Trans. AMS , 90 : 527 – 552 .
  • Wagner , K. 1970 . Graphentheorie , Mannheim .
  • Welsh , D.J.A. 1976 . Matroïd theory London
  • Wiedemann , A. and Roggenkamp , K.W. 1983 . Path orders of global dimension two . J. Alg , 80 : 113 – 133 .
  • Zavadskij , A.G. and Kirichenko , V.V. 1976 . Torsion-free modules over primary rings . Zap. Nauchn. Sem. LOMI im. V.A. Steklova AN SSSR , 57 : 100 – 116 . = J. Soviet. Math. 11(1979) 598 - 612

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.