Email this article A Remark on Commutative Arithmetic Rings
- Authors: Golod E.S.1
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Affiliations:
- Moscow State University
- Issue: Vol 213, No 2 (2016)
- Pages: 143-144
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237144
- DOI: https://doi.org/10.1007/s10958-016-2706-4
- ID: 237144
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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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About the authors
E. S. Golod
Moscow State University
Author for correspondence.
Email: moizhess@crc.umos.ru
Russian Federation, Moscow
