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Paper   IPM / M / 14867
School of Mathematics
  Title:   Characterizations of graded Prufer ∗-multiplication domains, II
  Author(s):  Parviz Sahandi
  Status:   To Appear
  Journal: Bull. Iranian Math. Soc.
  Supported by:  IPM
Let R=⊕α ∈ ΓRα be a graded integral domain and ∗ be a semistar operation on R. For aR, denote by C(a) the ideal of R generated by homogeneous components of a and forf=f0+f1X+…+fnXnR[X], let \Af:=∑i=0nC(fi). Let N(∗):={fR[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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