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Articles

Decomposition of modules into modules whose annihilators are pseudo-irreducible

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Pages 4616-4624 | Received 28 Sep 2017, Published online: 23 Apr 2018

References

  • Abuhlail, J. Y. (2015). Zariski topologies for coprime and second submodules. Algebra Colloq. 22(1):47–72.
  • Al-Shaniafi, Y., Smith, P. F. (2011). Comultiplication modules over commutative rings. J. Commut. Algebra 3(1):1–29.
  • Ansari-Toroghy, H., Farshadifar, F. (2007). The dual notion of multiplication modules. Taiwanese J. Math. 11(4):1189–1201.
  • Ansari-Toroghy, H., Farshadifar, F. (2008). On comultiplication modules. Korean Ann. Math. 25(2):57–66.
  • Ansari-Toroghy, H., Farshadifar, F. (2012). On the dual notion of prime submodules (II). Mediterr. J. Math. 9(2):327–336.
  • Ansari-Toroghy, H., Farshadifar, F. (2014). The Zariski topology on the second spectrum of a module. Algebra Colloq. 21(4):671–688.
  • Baeth, N. R., Geroldinger, A. (2014). Monoids of modules and arithmetic of direct-sum decompositions. Pac. J. Math. 271:257–319.
  • Birkenmeier, G. F., Ryan, C. E. (2016). Module decompositions using pairwise comaximal ideals. Commun. Algebra 44:4200–4211.
  • Facchini, A. (2012). Direct-sum decompositions of modules with semilocal endomorphism rings. Bull. Math. Sci. 2(2):225–279.
  • Frobenius, G., Stickelberger, L. (1879). Über gruppen von vertauschbaren elementen. J. Reine Angew. Math. 86:217–262.
  • Hedayat, S., Rostami, E. (2017). Decomposition of ideals into pseudo irreducible ideals. Commun. Algebra 45(4):1711–1718.
  • Hedayat, S., Rostami, E. (2018). A characterization of commutative rings whose maximal ideal spectrum is Noetherian. J. Algebra Appl. 17(1):1850003(8 pp.).
  • Juett, J. R. (2012). Generalized comaximal factorization of ideals. J. Algebra 352:141–166.
  • Macdonald, I. G. (1973). Secondary representation of modules over a commutative ring. Sympos. Math. XI:23–43.
  • McAdam, S., Swan, R. G. (2004). Unique comaximal factorization. J. Algebra 276:189–192.
  • Nikseresht, A., Sharif, H. (2014). On comultiplication and R-multiplication modules. J. Algebr. Syst. 2(1):1–19.
  • Ohm, J., Pendleton, R. L. (1968). Rings with Noetherian spectrum. Duke Math. J. 35:631–639.
  • Yassemi, S. (2001). The dual notion of prime submodules. Arch. Math (Brno) 37(4):273–278.

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