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