Advanced search
Publication Cover
Communications in Algebra Volume 35, 2007 - Issue 10
Submit an article Journal homepage
74
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Representations of Finite Posets Over Discrete Valuation Rings

David M. Arnold Department of Mathematics, Baylor University, Waco, Texas, USACorrespondence[email protected]
&
Daniel Simson Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland
Pages 3128-3144 | Received 03 Apr 2006, Published online: 25 Sep 2007

REFERENCES

  • Anderson , F. W. , Fuller , K. R. ( 1974 ). Rings and Categories of Modules . New York : Springer-Verlag .
  • Arnold , D. ( 2000 ). Abelian Groups and Representations of Finite Partially Ordered Sets . CMS Books in Math. New York : Springer .
  • Arnold , D. , Simson , D. ( 2005 ). Endo-wild representation type and generic representations of finite posets . Pacific J. Math. 219 : 101 – 126 .
  • Arnold , D. , Simson , D. ( 2006 ). Representations of finite partially ordered sets over commutative artinian uniserial rings . J. Pure Appl. Alg. 205 : 640 – 659 .
  • Atiyah , M. F. , MacDonald , I. G. ( 1969 ). Introduction to Commutative Algebra . Reading , Massachusetts : Addison-Wesley .
  • Brenner , S. ( 1974 ). Decomposition properties of some small diagrams of modules . Symposia Mathematica (Rome, 1972) . Vol. 13 . London : Academic Press , pp. 127 – 141 .
  • Kleiner , M. M. ( 1972 ). Partially ordered sets of finite type . In Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklova (LOMI) 28 : 32 – 41 (in Russian) .
  • Nazarova , L. A. ( 1975 ). Partially ordered sets of infinite type . Izv. Akad. Nauk SSSR. 39 : 963 – 991 (in Russian) .
  • Nazarova , L. A. , Roiter , A. V. ( 1972 ). Representations of partially ordered sets . In Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklova (LOMI) 28 : 5 – 31 (in Russian) .
  • Plahotnik , V. V. ( 1976 ). Representations of partially ordered sets over commutative rings . Izv. Akad. Nauk SSSR. 40 : 527 – 543 (in Russian) .
  • Ringel , C. , Schmidmeier , M. ( 2006 ). Submodule categories of wild representation type . Journal of Pure and Applied Algebra 205 ( 2 ): 412 – 422 .
  • Richman , F. ( 1995 ). Isomorphism of Butler groups at a prime p . Abelian Group Theory Cont. Math. 171 : 333 – 337 .
  • Richman , F. , Walker , E. ( 1999 ). Subgroups of p 5-bounded groups . in Abelian Groups and Modules . Boston : Birkhaüser , pp. 55 – 74 .
  • Simson , D. ( 1992 ). Linear Representations of Partially Ordered Sets and Vector Space Categories . Philadelphia : Gordon and Breach .
  • Simson , D. ( 1996 ). Socle projective representations of partially ordered sets and Tits quadratic forms with applications to lattices over orders . Abelian Groups and Modules . Vol. 182 . Lecture Notes in Pure and Applied Mathematics . New York : Marcel Dekker , pp. 73 – 112 .
  • Communicated by K. M. Rangaswamy.

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.