Unique factorization in polynomial rings with zero divisors

DOI10.1142/S0219498821501139zbMath1468.13013arXiv1906.00522OpenAlexW3012366788MaRDI QIDQ4997980

Ranthony A. C. Edmonds, Daniel D. Anderson

Publication date: 1 July 2021

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.00522

zbMATH Keywords

polynomial ringirreducible elementunique factorization ring

Mathematics Subject Classification ID

Polynomials over commutative rings (13B25) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Divisibility and factorizations in commutative rings (13A05)

Related Items

Unique factorization properties in commutative monoid rings with zero divisors, Associates, irreducibility, and factorization length in monoid rings with zero divisors, Finite factorization properties in commutative monoid rings with zero divisors

Cites Work

• Associate elements in commutative rings
• Factorization in integral domains
• On the divisors of monic polynomials over a commutative ring
• Factorization in commutative rings with zero divisors
• Sets of lengths of powers of a variable
• Polynomial extensions of atomic domains
• Spontaneous atomicity for polynomial rings with zero-divisors
• Non-Unique Factorization of Polynomials Over Residue Class Rings of the Integers
• Reduced Factorizations in Commutative Rings with Zero Divisors
• Unique Factorization Rings with Zero Divisors
• Unique factorization rings with zero divisors
• ACCP in Polynomial Rings: A Counterexample
• On Finite Factorization Rings
• Bounded Factorization Rings
• Factorization in commutative rings with zero divisors. III
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item