185
Views
0
CrossRef citations to date
0
Altmetric
Articles

The isomorphism problem for uniserial modules over an arbitrary ring

, &
Pages 4027-4036 | Received 11 Nov 2018, Accepted 08 Apr 2020, Published online: 22 Apr 2020

References

  • Auslander, M., Reiten, I., SmalØ, S. O. (1997). Representation Theory of Artin Algebras. Cambridge, UK: Cambridge University Press.
  • Boldt, A., Mojiri, A. (2008). On uniserial modules in the Auslander-Reiten quiver. J. Algebra 319(5):1825–1850. DOI: 10.1016/j.jalgebra.2007.11.026.
  • Bongartz, K. (1997). A note on algebras of finite uniserial type. J. Algebra 188(2):513–515. DOI: 10.1006/jabr.1996.6845.
  • Bongartz, K., Huisgen-Zimmermann, B. (2001). Varieties of uniserial representations IV. Kinship to geometric quotients. Trans. Amer. Math. Soc. 353(05):2091–2113. DOI: 10.1090/S0002-9947-01-02712-X.
  • Brooksbank, P. A., Wilson, J. B. (2015). The module isomorphism problem revisited. J. Algebra 421:541–559. DOI: 10.1016/j.jalgebra.2014.09.004.
  • Bumby, R. (1965). Modules which are isomorphic to submodules of each other. Arch. Math. 16(1):184–185. DOI: 10.1007/BF01220018.
  • Facchini, A. (1984). Lattice of submodules and isomorphism of subquotients. In: Göbel, R., Metelli, C., Orsatti, A., Salce, L. eds. Abelian Groups and Modules. International Centre for Mechanical Sciences (Courses and Lectures), vol 287. Vienna: Springer-Verlag. p. 491–501.
  • Facchini, A., Salce, L. (1990). Uniserial modules: sums and isomorphisms of subquotients. Commun. Algebra 18(2):499–517. DOI: 10.1080/00927879008823928.
  • Guil Asensio, P. A., Kalebogˇaz, B., Srivastava, A. K. (2018). The Schröder-Bernstein problem for modules. J. Algebra 498:153–164. DOI: 10.1016/j.jalgebra.2017.11.029.
  • Huisgen-Zimmermann, B. (1998). The geometry of uniserial representations of finite dimensional algebras I. J. Pure Appl. Algebra 127(1):39–72. DOI: 10.1016/S0022-4049(96)00184-3.
  • Mojiri, A. (2003). Geometric aspects of finite dimensional algebras-uniserial representations. M.Sc. Thesis. University of Ottawa, Ottawa, Canada.
  • Osofsky, B. An Example of a Cyclic Artinian Module of Infinite Length, unpublished (communicated by D. Eisenbud to C. Menini).
  • Příhoda, P. (2006). On uniserial modules that are not quasi-small. J. Algebra 299(1):329–343. DOI: 10.1016/j.jalgebra.2005.11.010.
  • Schiffler, R. (2014). Quiver Representations. Switzerland: Springer International Publishing.

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.