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 \(i\ne j\).
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Parkash, A. One dimensional local domains and radical formula. Beitr Algebra Geom 56, 729–733 (2015). https://doi.org/10.1007/s13366-014-0189-3
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DOI: https://doi.org/10.1007/s13366-014-0189-3