162
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

The cancellation property of rings

Pages 780-791 | Received 06 May 2015, Published online: 30 Jun 2017

References

  • Ara, P. (1996). Strongly π-regular rings have stable range one. Proc. Am. Math. Soc. 124(11):3293–3298.
  • Ara, P., Pedersen, G. K., Perera, F. (2000). An infinite analogue of rings with stable rank one. J. Algebra 230:608–655.
  • Chen, H. (2000). On stable range conditions. Commun. Algebra 28:3913–3924.
  • Cohn, P. M. (1956). The complement of a finitely generated direct summand of an abelian group. Proc. Am. Math. Soc. 7:520–521.
  • Crawley, P. (1965). The cancelllation of torsion abelian groups in direct sums. J. Algebra 2:432–442.
  • Evans, E. G., JR., (1973). Krull-Schmidt and cancellation over local rings. Pacific J. Math. 46(1):115–121.
  • Fuchs, L., Loonstra, F. (1971). On the cancellation of modules in direct sums over Dedekind domains. Indagationes Math. 74:163–169.
  • Goodearl, K. R. (1976). Power-cancellation of groups and modules. Pacific J. Math. 94(2):387–411.
  • Goodearl, K. R. (1984). Cancellation of low-rank vector bundles. Pacific J. Math. 113:289–302.
  • Goodearl, K. R., Menal, P. (1988). Stable range one for rings with many units. J. Pure Appl. Algebra 54:261–287.
  • Hsü, C. S. (1962). Theorems on direct sums of modules. Proc. Am. Math. Soc. 13:540–542.
  • Jósson, B., Tarski, A. (1947). Direct Decompositions of Finite Algebraic Systems, Notre Dame Mathematical Lectures, Number 5, Indiana: University of Notre Dame.
  • Kaplansky, I. (1952). Modules over Dedekind rings and valuation rings. Trans. Am. Math. Soc. 72:327–340.
  • Lam, T. Y. (2006). Serre’s Problem on Projective Modules, Springer Monograph in Mathematics. Berlin, Heidelberg, New York: Springer Verlag.
  • Magurn, B. A. (2002). An Algebraic Introduction to K-Theory. Cambridge, UK: Cambridge University Press.
  • Quillen, D. (1976). Projective modules over polynomial rings. Invent. Math. 36:167–171.
  • Rotman, J., Yen, T. (1961). Modules over a complete valuation rings. Trnas. Am. Math. Soc. 98:242–254.
  • Suslin, A. A. (1976). Projective modules over a polynomial ring are free. Soviet Math. Dokl. 17:1160–1164.
  • Tong, W. T. (2005). Algebraic K-Theory (in Chinese). Nanjing, P.R. China: Nanjing University Press.
  • Vaserstein, L. N. (1984). Bass’s first stable range condition. J. Pure Appl. Algebra 34:319–330.
  • Walker, E. A. (1956). Cancellation in direct sums of groups. Proc. Am. Math. Soc. 7:898–902.
  • Warfield, R. B., JR., (1980). Cancellation of modules and stable range of endomorphism rings. Pacific J. Math. 91(2):457–485.
  • Zhang, H., Tong, W. T. (2005). The cancellable range of rings. Arch. der Math. 85:327–334.
  • Zhang, H., Tong, W. T. (2006). The cancellation property of projective modules. Algebra Colloquium 13(4):617–622.
  • Zhang, H., Tong, W. T. (2006). Weakly stable modules. Commun. Algebra 34:983–989.

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.