63
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

DIRECT SUM DECOMPOSITION OF THE PRODUCT OF PREINJECTIVE MODULES OVER RIGHT PURE SEMISIMPLE HEREDITARY RINGS

Pages 3037-3043 | Received 01 Jan 2001, Published online: 01 Sep 2006

REFERENCES

  • Simson , D. 2000 . An Artin Problem for Division Ring Extensions and the Pure Semisimplicity Conjecture, II . J. Algebra , 227 : 670 – 705 .
  • Simson , D. 2001 . On Small Right Pure Semisimple Rings and the Structure of their Auslander-Reiten Quiver . Communic. in Algebra , 29 in press
  • Simson , D. 1992 . Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic and Applications Vol. 4 , Switzerland, Australia : Gordon and Breach Science Publishers .
  • Simson , D. 1977 . Pure Semisimple Categories and Rings of Finite Representation Type . J. Algebra , 48 : 290 – 296 .
  • 1980 . Corrigendum . J. Algebra , 67 : 254
  • Simson , D. 1996 . An Artin Problem for Division Ring Extensions and the Pure Semisimplicity Conjecture, I . Arch. Math. , 66 : 114 – 122 .
  • Auslander , M. 1974 . Representation Theory of Artin Algebras II . Communic. in Algebra , 1 : 269 – 310 .
  • Ringel , C.M. and Tachikawa , H. 1975 . QF-3 Rings . J. Reine Angew. Math. , 272 : 49 – 72 .
  • Auslander , M. 1976 . Algebra, Topology and Category Theory Edited by: Heller , A. and Tierney , M. 3 – 17 . New York : Academic Press .
  • Simson , D. 1981 . Partial Coxeter Functors and Right Pure Semisimple Hereditary Rings . J. Algebra , 71 : 195 – 218 .
  • Simson , D. 1997 . “ A Class of Potential Counter-examples to the Pure Semisimplicity Conjecture ” . In Advances in Algebra and Model Theory Edited by: Droste , M. and Göbel , R. Vol. 9 , 345 – 373 . Amsterdam : Gordon and Breach Sci. Publishers . Algebra, Logic, and Applications
  • Simson , D. 1999 . On the Representation Theory of Artinian Rings and Artin's Problems on Division Ring Extensions . Bull. Greek Math. Soc. , 42 : 97 – 112 .
  • Simson , D. 1995 . On Right Pure Semisimple Hereditary Rings and an Artin Problem . J. Pure Appl. Algebra , 104 : 313 – 332 .
  • Okoh , F. 1992 . Direct Sums and Direct Products of Finite-dimensional Modules over Path Algebras . J. Algebra , 151 : 487 – 501 .
  • Lenzing , H. and Okoh , F. Separable Modules over a Canonical Algebra . Canad. Math. Soc. Proc. Series . 1992 , Ottawa . Edited by: Dlab , V. and Lenzing , H. Vol. 14 , pp. 339 – 352 .
  • Huisgen-Zimmermann , B. and Okoh , F. 2001 . Direct Product of Modules and the Pure Semisimplicity Conjecture . Communic. in Algebra , 29 ( 1 ) : 271 – 276 .
  • Simson , D. 1974 . Functor Categories in which Every Flat Object is Projective . Bull. Polon. Acad. Sci., Ser. Math. , 22 : 375 – 380 .
  • Simson , D. 1977 . On Pure Global Dimension of Locally Presented Grothendieck Categories . Fund. Math. , 96 : 91 – 116 .
  • Crawley-Boevey , W. 1993 . Matrix Representations for Artinian Rings and an Application to Rings of Finite Representation Type . J. Algebra , 157 : 1 – 25 .
  • Anderson , F. and Fuller , K. 1992 . “ Rings and Categories of Modules ” . 2 Vol. 13 , New York : Springer Verlag . Graduate Texts in Mathematics

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.