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| Paper IPM / M / 14867 |
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| Abstract: | |
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Let R=⊕α ∈ ΓRα be a graded integral domain and ∗ be a semistar operation on R. For a ∈ R, denote by C(a) the ideal of R generated by homogeneous components of a and forf=f0+f1X+…+fnXn ∈ R[X], let \Af:=∑i=0nC(fi). Let N(∗):={f ∈ R[X] | f ≠ 0and\Af∗=R∗}. In this paper we study relationships between ideal theoretic properties of \NA(R,∗):=R[X]N(∗) and the homogeneous ideal theoretic properties of R. For example we show that R is a graded Prüfer-∗-multiplication domain if and only if \NA(D,∗) is a Prüfer domain if and only if \NA(R,∗) is a Bézout domain. We also determine when \NA(R,v) is a PID.
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