Relative Polynomial Closure and Monadically Krull Monoids of Integer-Valued Polynomials

DOI10.1007/978-3-319-38855-7_6zbMath1352.13013arXiv1409.1111OpenAlexW2972655437MaRDI QIDQ2826741

Sophie Frisch

Publication date: 18 October 2016

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.1111

zbMATH Keywords

factorizationsmonoidsKrull monoidsinteger-valued polynomialsdivisor homomorphismpolynomial closurepolynomially dense

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in number theory (11C08) Polynomials over commutative rings (13B25) Polynomials (irreducibility, etc.) (11R09) Divisibility and factorizations in commutative rings (13A05) Arithmetic theory of semigroups (20M13)

Related Items (7)

Split absolutely irreducible integer-valued polynomials over discrete valuation domains ⋮ Divisor sequences of atoms in Krull monoids ⋮ Sets of Lengths ⋮ Absolute irreducibility of the binomial polynomials ⋮ Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields ⋮ Characterizing absolutely irreducible integer-valued polynomials over discrete valuation domains ⋮ Strong atoms in monadically Krull monoids

Cites Work

• Sets that determine integer-valued polynomials
• On a theorem of R. Gilmer
• Polynomial closure
• Polynomial closure in essential domains
• Substitution and closure of sets under integer-valued polynomials

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