“…Let M be an R−module. An element x of R is said to be tight dependent on I relative to M if there exists an element c ∈ R • such that (0 : M I[q] ) ⊆ (0 : M cx q ) f or all q 0.It has been proved thatI * [M ] = {x ∈ R : x is tight dependent on I relative to M }is an ideal of R (see[2]). The ideal I* [M ] is called the tight closure of I relative to M .…”
In this paper we will define the tight integral closure of a finite set of ideals of a ring relative to a module and we will study some related results.
“…Let M be an R−module. An element x of R is said to be tight dependent on I relative to M if there exists an element c ∈ R • such that (0 : M I[q] ) ⊆ (0 : M cx q ) f or all q 0.It has been proved thatI * [M ] = {x ∈ R : x is tight dependent on I relative to M }is an ideal of R (see[2]). The ideal I* [M ] is called the tight closure of I relative to M .…”
In this paper we will define the tight integral closure of a finite set of ideals of a ring relative to a module and we will study some related results.
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