2016/10/16 by Parviz Sahandi, Sahandi, Parviz
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC
paper · pdf · doi:10.48550/arxiv.1610.04845
Bull. Iranian Math. Soc. to appear
arxiv created 2017/07/30 · arxiv updated 2017/08/01
Let R=\bigoplusα∈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.