Generalized factorials and fixed divisors over subsets of a Dedekind domain

DOI10.1006/jnth.1998.2220zbMath0931.13004OpenAlexW2071154322MaRDI QIDQ1273198

Manjul Bhargava

Publication date: 23 February 2000

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/91d91c7114ed5ef7a59e21ffbf334303978348a7

zbMATH Keywords

Dedekind domainprimitive polynomialfixed divisorfactorial ideal

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Polynomials over commutative rings (13B25) Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (26)

On Least Common Multiples of Polynomials inZ/nZ[x] ⋮ Bhargava factorials and irreducibility of integer-valued polynomials ⋮ Bhargava’s Early Work: The Genesis of <em>P</em>-Orderings ⋮ What You Should Know About Integer-Valued Polynomials ⋮ On Bhargava's factorials of the set of twin primes in ℤ and in 𝔽_q[T] ⋮ Integer-Valued Polynomials: Looking for Regular Bases (A Survey) ⋮ On the Bhargava factorial of polynomial maps ⋮ The factorial function and generalizations, extended ⋮ Probabilities and Fixed Divisors of Integer Polynomials ⋮ Regular subsets of valued fields and Bhargava's \(v\)-orderings ⋮ Pólya fields, Pólya groups and Pólya extensions: a question of capitulation ⋮ From Pólya fields to Pólya groups (II) non-Galois number fields ⋮ Asymptotic behavior of characteristic sequences of integer-valued polynomials ⋮ Minimal Generating Sets for the D-Algebra Int(S, D) ⋮ Fixed Divisor of a Multivariate Polynomial and Generalized Factorials in Several Variables ⋮ Simultaneous orderings in function fields ⋮ An overview of some recent developments on integer-valued polynomials: Answers and Questions ⋮ About Number Fields with Pólya Group of Order $$\le $$ ≤ 2 ⋮ From Pólya fields to Pólya groups. I: Galois extensions ⋮ Newtonian and Schinzel sequences in a domain ⋮ A survey on fixed divisors ⋮ Irreducible polynomials and full elasticity in rings of integer-valued polynomials ⋮ $P$-orderings of noncommutative rings ⋮ Chinese remainder theorem for cyclotomic polynomials in \(\mathbb Z[X\)] ⋮ On systems of diagonal forms ⋮ \(P\)-orderings: A metric viewpoint and the non-existence of simultaneous orderings.

Cites Work

• On a class of ideals in an algebraic number field
• On polynomials with integer coefficients
• P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.

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