多项式型扩张的弹性
Elasticity in polynomial-type extensions
摘要：
原子整环的弹性，在某种意义上，是一个度量域距离唯一因子分解域（或者更恰当地说，半因子域）有多远。本文考虑区域R的弹性与其多项式环R[x]的弹性之间的关系。例如，如果R至少有一个原子，多项式环R[x]具有弹性1的充分条件是R[x]中的每个非常数不可约多项式f在K[x]中不可约。我们将确定其多项式环满足这个条件的整环R。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
