A Remark on Commutative Arithmetic Rings

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• 作者：E. S. Golod
• 刊名：Journal of Mathematical Sciences
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：213
• 期：2
• 页码：143-144
• 全文大小：83 KB
• 参考文献：1.A. A. Tuganbaev, Ring Theory. Arithmetical Modules and Rings [in Russian], MCCME, Moscow (2009).
  
• 作者单位：E. S. Golod (1)
  
  1. Moscow State University, Moscow, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-8795

文摘

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