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Elasticity in Polynomial-Type Extensions

Part of: Arithmetic rings and other special rings

Published online by Cambridge University Press:  28 March 2016

Mark Batell  and
Jim Coykendall
Mark Batell
Affiliation:
Department of Mathematics, North Dakota State University, Fargo, ND 58108, USA
Jim Coykendall
Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA ([email protected])
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Abstract

The elasticity of an atomic integral domain is, in some sense, a measure of how far the domain is from being 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 non-constant irreducible polynomial f ∈ R[x] be irreducible in K[x]. We will determine the integral domains R whose polynomial rings satisfy this condition.

Keywords

factorizationunique factorizationpolynomialsAP-domainGL-domain

MSC classification

Secondary: 13F15: Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 3 , August 2016 , pp. 581 - 590
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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