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Research Article

On generalizations of classical primary submodules over commutative rings

ORCID Icon & | (Reviewing Editor)
Article: 1458556 | Received 03 Dec 2017, Accepted 21 Mar 2018, Published online: 29 Apr 2018

References

  • Anderson, D. D., & Bataineh, M. (2008). Generalizations of prime ideals. Communications in Algebra, 36, 686–696.10.1080/00927870701724177
  • Anderson, D. F., & Badawi, A. (2011). On n-absorbing ideals of commutative rings. Communications in Algebra, 39, 1646–1672.10.1080/00927871003738998
  • Arabi-Kakavand, M., & Behboodi, M. (2014). Modules whose classical prime submodules are intersections of maximal submodules. Bulletin of the Korean Mathematical Society, 51(1), 253–266.10.4134/BKMS.2014.51.1.253
  • Atani, S. E., & Farzalipour, F. (2005). On weakly primary ideals. Glasgow Mathematical Journal, 12(3), 423–429.
  • Azizi, A. (2006). Weakly prime submodules and prime submodules. Glasgow Mathematical Journal, 48, 343–346.10.1017/S0017089506003119
  • Azizi, A. (2008). On prime and weakly prime submodules. Vietnam Journal of Mathematics, 36(3), 315–325.
  • Baziar, M., & Behboodi, M. (2009). Classical primary submodules and decomposition theory of modules. Journal of Algebra and Its Applications, 8(3), 351–362.10.1142/S0219498809003369
  • Badawi, A., Tekir, U., Ugurlu, E. A., Ulucak, G., & Celikel, E. Y. (2016). Generalizations of 2-absorbing primary ideals of commutative rings. Turkish Journal of Mathematics, 40, 703–717.10.3906/mat-1505-43
  • Badawi, A., Tekir, U., & Yetkin, E. (2015). On weakly 2-absorbing primary ideals of commutative rings. Journal of the Korean Mathematical Society, 52(1), 97–111.10.4134/JKMS.2015.52.1.097
  • Bataineh, M., & Khuhail, S. (2011). Generalizations of primary ideals and submodules. International Journal of Contemporary Mathematical Sciences, 6(17), 811–824.
  • Behboodi, M. (2006). On weakly prime radical of modules and semi-compatible modules. Acta Mathematica Hungarica, 113(3), 239–250.
  • Behboodi, M. (2007). A generalization of baer’s lower nilradical for modules. Journal of Algebra and Its Applications, 6(2), 337–353.10.1142/S0219498807002284
  • Behboodi, M., Jahani-Nezhad, R., & Naderi, M. H. (2011). Classical quasi-primary submodules. Bulletin of the Iranian Mathematical Society, 37(4), 51–71.
  • Behboodi, M., & Shojaee, S. H. (2010). On chains of classical prime submodules and dimension theory of modules. Bulletin of the Iranian Mathematical Society, 36(1), 149–166.
  • Darani, A. Y. (2012). Generalizations of primary ideals in commutative rings. Novi Sad Journal of Mathematics, 42(1), 27–35.
  • Ebrahimpour, M., & Mirzaee, F. (2017). On ϕ-semeprime submodules. Journal of the Korean Mathematical Society, 54(4), 1099–1108.
  • El-Bast, Z. A., & Smith, P. F. (1988). Multiplication modules. Communications in Algebra, 16(4), 755–779.10.1080/00927878808823601
  • Larsen, M., & McCarthy, P. (1971). Multiplicative theory of ideals. New York, NY: Academic Press.
  • Mostafanasab, H. (2015). On weakly classical primary submodules. Bulletin of the Belgian Mathematical Society—Simon Stevin, 22(5), 743–760.
  • Mostafanasab, H., Tekir, U., & Oral, K. H. (2016). Weakly classical prime submodules. Kyungpook Mathematical Journal, 56, 1085–1101.10.5666/KMJ.2016.56.4.1085
  • Sharp, R. (2000). Steps in commutative algebra. Cambridge: Cambridge University Press.
  • Tekir, U., Koc, S., & Oral, K. H. (2016). On 2-absorbing quasi-primary ideals in commutative rings. Communications in Mathematics and Statistics, 4, 55–62.10.1007/s40304-015-0075-9
  • Yılmaz, E., & Cansu, S. K. (2014). Baer’s lower nilradical and classical prime submodules. Bulletin of the Iranian Mathematical Society, 40(5), 263–1274.
  • Zamani, N. (2010). ϕ-prime submodules. Glasgow Mathematical Journal, 52(2), 253–259.10.1017/S0017089509990310