A Remark on Commutative Arithmetic Rings

E. S. Golod

doi:10.1007/s10958-016-2706-4

A Remark on Commutative Arithmetic Rings

Authors: Golod E.S.¹
Affiliations:
1. 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.

Keywords

Russia, Local Ring, Maximal Ideal, Commutative Ring, Ring Theory

About the authors

E. S. Golod

Moscow State University

Author for correspondence.
Email: moizhess@crc.umos.ru
Russian Federation, Moscow

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