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- W139378311 abstract "This paper studies the Ratliff-Rush closure and the integral closure of an ideal in a valuation and Prufer domains. By definition, the Ratliff-Rush closure (respectively the integral closure) of an ideal $I$ of a domain $R$ is the ideal given by $tilde{I}:=bigcup(I^{n+1}:_{R}I^{n})$ (respectively $I':={xin R| x$ satisfies an equation of the form $x^{k}+ a_{1}x^{k-1}+... + a_{k}=0$, where $a_{i}in I^{i}$ for each $iin {1, ..., k}}$). An ideal $I$ is said to be a Ratliff-Rush (respectively integrally closed) ideal if $tilde{I}=I$ (respectively $I=I'$). We completely characterize valuation and Prufer domains such that every ideal is a Ratliff-Rush ideal, and domains for which each ideal generated by two elements is integrally closed." @default.
- W139378311 created "2016-06-24" @default.
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- W139378311 date "2007-05-29" @default.
- W139378311 modified "2023-09-27" @default.
- W139378311 title "Ratliff-Rush and Integral Closure of Ideals in a Valuation and Prufer Domains" @default.
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