Ấn phẩm:
Integer-valued polynomials and pullbacks of arithmetical rings
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Let D be an integral domain with field of fractions K, and let E be a non-empty finite subset of D. For n > 2, we show that the n-generator property forD is equivalent to the n-generator property for Int(E, D), which is equivalent to strong (n + 1)-generator property for Int(E, D). We also give necessary and sufficient conditions that the pullback of a conductor square be a chain ring (that is, a ring whose ideals are totally ordered by inclusion), and we give necessary and sufficient conditions that the pullback of a conductor square be an arithmetical ring (that is, a ring which is locally a chain ring at every maximal ideal). We characterize all Priifer domains R between D[X] and K[X] such that the conductor C of K[X] into R is non-zero. As an application, we show that for n > 2, such a ring R has the n-generator property (every finitely generated ideal can be generated by n elements) if and only if R/C has the same property.
Tác giả
Boynton, Jason
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Nơi xuất bản
Nhà xuất bản
Florida Atlantic University
Năm xuất bản
2006
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Từ khóa chủ đề
Ring (Toán học) , Đa thức