The ratliff-rush ideals in a noetherian ring
نویسندگان
چکیده
منابع مشابه
Ratliff-rush Closure of Ideals in Integral Domains
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 := S (I :R I ) and an ideal I is said to be a Ratliff-Rush ideal if Ĩ = I. We completely characterize integrally closed domains in which every ideal is a Ratliff-Rush ideal and we give a complete description of the Ratliff-Rush cl...
متن کاملTopics on the Ratliff-Rush Closure of an Ideal
Introduction Let be a Noetherian ring with unity and be a regular ideal of , that is, contains a nonzerodivisor. Let . Then . The :union: of this family, , is an interesting ideal first studied by Ratliff and Rush in [15]. The Ratliff-Rush closure of is defined by . A regular ideal for which is called Ratliff-Rush ideal. The present paper, reviews some of the known prop...
متن کاملRatliff-rush and Integral Closure of Ideals in a Valuation and Prüfer Domains
This paper studies the Ratliff-Rush closure and the integral closure of an ideal in a valuation and Prüfer domains. By definition, the RatliffRush closure (respectively the integral closure) of an ideal I of a domain R is the ideal Given by Ĩ := S (I :R I ) (respectively I := {x ∈ R|x satisfies an equation of the form x + a1x + · · ·+ ak = 0, where ai ∈ I i for each i ∈ {1, . . . , k}}). An ide...
متن کاملRatliff-rush and Integral Closures of Ideals in a Valuation and Prüfer Domains
This paper studies the Ratliff-Rush closure and the integral closure of an ideal in a valuation and Prüfer domains. By definition, the RatliffRush closure (respectively the integral closure) of an ideal I of a domain R is the ideal given by Ĩ := S (I :R I ) (respectively I := {x ∈ R|x satisfies an equation of the form x + a1x + · · ·+ ak = 0, where ai ∈ I i for each i ∈ {1, . . . , k}}). An ide...
متن کاملOn the Computation of Ratliff-rush Closure
Let R be a Cohen-Macaulay local ring with maximal ideal m. In this paper we present a procedure for computing the Ratllif-Rush closure of a m−primary ideal I ⊂ R.
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 1992
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927879208824359