Elasticity in polynomial-type extensions

2013/02/19 by Batell, Mark, Coykendall, Jim · 1 citation
#13A05 #13B25 #13F15 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1302.4766

Abstract

The elasticity of an atomic integral domain is, in some sense, a measure of how far the domain is from being a unique factorization domain (or, more properly, a half-factorial domain). We consider the relationship between the elasticity of a domain, R, and the elasticity of its polynomial ring R[x]. For example, if R has at least one atom, a sufficient condition for the polynomial ring R[x] to have elasticity 1 is that every nonconstant irreducible polynomial f in R[x] be irreducible in K[x]. We will determine the integral domains R whose polynomial rings satisfy this condition.

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• Multiplicative Relationships of Subrings and their Applications to Factorization

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