Graded Integral Domains and Nagata Rings , Ii
نویسندگان
چکیده
Let D be an integral domain with quotient field K, X be an indeterminate over D, K[X] be the polynomial ring over K, and R = {f ∈ K[X] | f(0) ∈ D}; so R is a subring of K[X] containing D[X]. For f = a0 + a1X + · · ·+ anX ∈ R, let C(f) be the ideal of R generated by a0, a1X, . . . , anX n and N(H) = {g ∈ R | C(g)v = R}. In this paper, we study two rings RN(H) and Kr(R, v) = { fg | f, g ∈ R, g 6= 0, and C(f) ⊆ C(g)v}. We then use these two rings to give some examples which show that the results of [4] are the best generalizations of Nagata rings and Kronecker function rings to graded integral domains.
منابع مشابه
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تاریخ انتشار 2017