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Information Journal Paper

Title

ON STRONGLY DENSE SUBMODULES

Pages

  731-747

Abstract

 The submodules with the property of the title (a submodule N of an R -module M is called strongly dense in M, denoted by N£sd M, if for any index set I, ΠIN£d ΠIM) are introduced and fully investigated. It is shown that for each submoduleN of M there exists the smallest subsetD′ ÍM such that N+D′ is a STRONGLY DENSE SUBMODULE of M and D′ ∩ N=0. We also introduce a class of modules in which the two concepts of strong essentiality and strong density coincide. It is also shown that for any module M, dense submodules in M are strongly dense if and only if M £sd ~E (M), where ~E (M) is the rational hull of M. It is proved that R has no strongly dense left ideal if and only if no nonzeroelement of every cyclic R -module M has a strongly dense annihilator in R. Finally, some properties and new concepts related to strong density are studied.

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    APA: Copy

    GHASHGHAEI, E., & NAMDARI, M.. (2016). ON STRONGLY DENSE SUBMODULES. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 42(3), 731-747. SID. https://sid.ir/paper/687719/en

    Vancouver: Copy

    GHASHGHAEI E., NAMDARI M.. ON STRONGLY DENSE SUBMODULES. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2016;42(3):731-747. Available from: https://sid.ir/paper/687719/en

    IEEE: Copy

    E. GHASHGHAEI, and M. NAMDARI, “ON STRONGLY DENSE SUBMODULES,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 42, no. 3, pp. 731–747, 2016, [Online]. Available: https://sid.ir/paper/687719/en

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