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A Remark on Commutative Arithmetic Rings

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Abstract

It is proved that a commutative ring with identity R is arithmetic (i.e., the ideal lattice of R is distributive) if and only if for any finitely generated (or any finitely presented) R-module M and any ideal I of R the equality I +AnnM = Ann(M/IM) holds.

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References

  1. A. A. Tuganbaev, Ring Theory. Arithmetical Modules and Rings [in Russian], MCCME, Moscow (2009).

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    E. S. Golod

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  1. E. S. Golod
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Correspondence to E. S. Golod.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 19, No. 2, pp. 21–23, 2014.

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Golod, E.S. A Remark on Commutative Arithmetic Rings. J Math Sci 213, 143–144 (2016). https://doi.org/10.1007/s10958-016-2706-4

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  • DOI: https://doi.org/10.1007/s10958-016-2706-4

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