One dimensional local domains and radical formula

Original Paper
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Abstract

If \((R, P)\) is a local domain of dimension one, then it is shown that \(R\) satisfies the radical formula if and only if \(( Ra _1: Ra _2+ Ra _3+\cdots + Ra _n)=P( Ra _1: Ra _2+ Ra _3+\cdots + Ra _n)\) for every integer \(n\ge 2\) and for every \(a_1, a_2,\ldots ,a_n\in R\) such that \(a_i\notin Ra _j\) for every \(i\ne j\).

Keywords

Prime submodules Radical formula Local rings Integral domains 

Mathematics Subject Classification (1991)

13C13 13C99 

References

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Copyright information

© The Managing Editors 2014

Authors and Affiliations

  1. 1.Discipline of MathematicsIndian Institute of Technology IndoreIndoreIndia

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