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Old problems and new questions around integer-valued polynomials and factorial sequences. (English) Zbl 1117.13022

Brewer, James W. (ed.) et al., Multiplicative ideal theory in commutative algebra. A tribute to the work of Robert Gilmer. New York, NY: Springer (ISBN 978-0-387-24600-0/hbk). 89-108 (2006).
The authors present several interesting open questions dealing with various aspects of the theory of integer-valued polynomials. These questions concern, in particular, Bhargava factorials [M. Bhargava, J. Reine Angew. Math. 490, 101–127 (1997; Zbl 0899.13022)], and Newtonian domains, defined as domains \(D\) which contain a sequence \(a_n\) such that the polynomials \(f_n(X)=\prod_{k=0}^{n-1}(X-a_k)/(a_n-a_k)\) form a basis for the module of all polynomials over \(K\), the field of quotients of \(D\), which map \(D\) in \(D\).
For the entire collection see [Zbl 1106.13001].

MSC:

13F20 Polynomial rings and ideals; rings of integer-valued polynomials
11B68 Bernoulli and Euler numbers and polynomials
11B83 Special sequences and polynomials
13B25 Polynomials over commutative rings
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations

Citations:

Zbl 0899.13022

Software:

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