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Original Articles

Commutative rings whose proper ideals are direct sums of uniform modules

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Pages 1277-1286 | Received 29 Jan 2017, Published online: 30 Aug 2017

References

  • Artin, E. (1927). Zur Theorie der hyperkomplexen Zahlen. Abh. Math. Sem. U. Hamburg 5:251–260.
  • Asano, K. (1939). Über verallgemeinerte Abelsche Gruppen mit hyperkomplexen Operatorenring und ihre Anwendungen. Jap J. Math. 15:231–253.
  • Behboodi, M., Ghorbani, A., Moradzadeh-Dehkordi, A. (2011). Commutative Noetherian local rings whose ideals are direct sums of cyclic modules. J. Algebra 345:257–265.
  • Behboodi, M., Heidari, S. Commutative rings all of whose proper ideals are serial. Algebr. Represent. Theory (to appear).
  • Behboodi, M., Heidari, S., Roointan-Isfahani, S. (2016). Commutative rings whose proper ideals are direct sums of completely cyclic modules. J. Algebra Appl. 15(8):1650160 ( 12 pages).
  • Behboodi, M., Shojaee, S. H. (2014). Commutative local rings whose ideals are direct sums of cyclic modules. Algebr. Represent. Theory 17:971–982.
  • Cohen, I. S. (1950). Commutative rings with restricted minimum condition. Duke Math. J. 17:27–42.
  • Cohen, I. S., Kaplansky, I. (1951). Rings for which every module is a direct sum of cyclic modules. Math. Z. 54:97–101.
  • Jain, S. K., Srivastava, A. K., Tuganbaev, A. A. (2012). Cyclic Modules and the Structure of Rings. Oxford: Oxford University Press.
  • Kaplansky, I. (1970). Commutative Rings. Boston: Allyn and Bacon.
  • Köthe, G. (1935). Verallgemeinerte Abelsche Gruppen mit hyperkomplexem Operatorenring (German). Math. Z. 39(1):31–44.
  • Lam, T. Y. (1998). Lectures on Modules and Rings. Graduate Texts in Mathematics, Vol. 189. Berlin, New York: Springer-Verlag.
  • Nakayama, T. (1941). On Frobeniusean algebras II. Ann. Math. 42(2):1–21.
  • Skornyakov, L. A. (1969). When are all modules semi-chained? Math. Z. 5:173–182.
  • Warfield, R. B. (1972). Rings whose modules have nice decompositions. Math. Z. 125:187–192.
  • Wedderburn, J. H. M. (1908). On hypercomplex numbers. On hypercomplex numbers s2–6(1):77–118.
  • Zariski, O., Samuel, P. (1960). Commutative Algebra, Vol. I. Princeton: Van Nostrand.

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