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Properties of a certain product of submodules

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Ukrainian Mathematical Journal Aims and scope

Let R be a commutative ring with identity, let M be an R-module, and let K 1, . . . ,K n be submodules of M: We construct an algebraic object called the product of K 1, . . . ,K n : This structure is equipped with appropriate operations to get an R(M)-module. It is shown that the R(M)-module M n  = M . . .M and the R-module M inherit some of the most important properties of each other. Thus, it is shown that M is a projective (flat) R-module if and only if M n is a projective (flat) R(M)-module.

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Authors and Affiliations

  1. Toosi University of Technology, Tehran, Iran

    M. J. Nikmehr, R. Nikandish & S. Heidari

Authors
  1. M. J. Nikmehr
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  2. R. Nikandish
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  3. S. Heidari
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 4, pp. 502–512, April, 2011.

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Nikmehr, M.J., Nikandish, R. & Heidari, S. Properties of a certain product of submodules. Ukr Math J 63, 580–595 (2011). https://doi.org/10.1007/s11253-011-0526-8

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  • DOI: https://doi.org/10.1007/s11253-011-0526-8

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