207
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Some new dimensions of modules and rings

, &
Pages 3353-3364 | Received 13 Jul 2016, Published online: 09 Jan 2017

References

  • Chase, S. U. (1960). Direct products of modules, Trans. Am. Math. Soc. 97:457–473. doi:10.1090/S0002-9947-1960-0120260-3
  • Clark, J., Lomp, C., Vanaja, N., Wisbauer, R. (2006). Lifting Modules. Supplements and Projectivity in Module Theory. Frontiers in Mathematics. Boston: Birkhäuser.
  • Facchini, A. (1998). Module Theory. Endomorphism Rings and Direct Sum Decompositions in Some Classes of Modules. Basel: Birkhäuser Verlag.
  • Ghorbani, A., Naji Esfahani, M. (2015). Local dimension of coatomic modules. Commun. Algebra 43(12):5205–5216. doi:10.1080/00927872.2014.974104
  • Ghorbani, A., Nazemian, Z. (2015). On commutative rings with uniserial dimension. J. Algebra Appl. 14(1):1550008-1–1550008-10. doi:10.1142/S0219498815500085
  • Goodearl, K. R. (1987). Surjective endomorphisms of finitely generated modules, Commun. Algebra 15:589–609. doi:10.1080/00927878708823433
  • Griffith, P. (1970). On the decomposition of modules and generalized left uniserial rings. Math. Ann. 184:300–308. doi:10.1007/BF01350858
  • Hirano, Y., Mogami, I. (1987). Modules whose proper submodules are non-hopf kernels. Commun. Algebra 15(8):1549–1567. doi:10.1080/00927878708823487
  • Lam, T. Y. (1999). Lectures on Modules and Rings. Graduate Texts in Mathematics, Vol. 189. New York: Springer.
  • Lam, T. Y. (2004). A crash course on stable range, cancellation, substitution, and exchange. J. Algebra Appl. 3:301–343. doi:10.1142/S0219498804000897
  • Nazemian, Z., Ghorbani, A., Behboodi, M. (2014). Uniserial dimension of modules. J. Algebra 399:894–903. doi:10.1016/j.jalgebra.2013.09.054
  • Puninski, G., Rothmaler, Ph. (1999). Rings described by various purities. Commun. Algebra 27(5):2127–2162. doi:10.1080/00927879908826554
  • Ribenboim, P. (1969). Rings and Modules. Interscience Tracts in Pure and Applied Mathematics, Vol. 24. New York: Interscience Publishers.
  • Sarath, B., Varadarjan, K. (1979). Dual Goldie dimension II. Commun. Algebra 7(17):1885–1899. doi:10.1080/00927877908822434
  • Wisbauer, R. (1991). Foundations of Module and Ring Theory. Philadelphia: Gordon and Breach.

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.