Geodesic
RATLIFF–RUSH CLOSURE OF IDEALS IN INTEGRAL DOMAINS
Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 681-689

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DOI

This paper studies the Ratliff–Rush closure of ideals in integral domains. By definition, the Ratliff–Rush closure of an ideal I of a domain R is the ideal given by Ĩ := ∪(In+1 :R In), and an ideal I is said to be a Ratliff–Rush ideal if Ĩ = I. We completely characterise integrally closed domains in which every ideal is a Ratliff–Rush ideal, and we give a complete description of the Ratliff–Rush closure of an ideal in a valuation domain.
DOI : 10.1017/S0017089509990097
Mots-clés : Primary 13A15, 13A18, 13F05, secondary 13G05, 13F30 
MIMOUNI, A. RATLIFF–RUSH CLOSURE OF IDEALS IN INTEGRAL DOMAINS. Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 681-689. doi: 10.1017/S0017089509990097
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     title = {RATLIFF{\textendash}RUSH {CLOSURE} {OF} {IDEALS} {IN} {INTEGRAL} {DOMAINS}},
     journal = {Glasgow mathematical journal},
     pages = {681--689},
     year = {2009},
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     doi = {10.1017/S0017089509990097},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509990097/}
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