Elasticity of factorizations in \(R_{0}+XR_{1}+\cdots +X^{l}R_{l}[X]\)
The author considers domains \(D=R_0+XR_1+\cdots+X^{l-1}R_{l-1}+X^lR_l[X]\), where \(R_0\subset R_1\subset \dots\subset R_l\) are finitely generated domains, with \(R_l\) integral over \(R_0\). A necessary and sufficient condition is given for the finiteness of elasticity of \(D\), defined as \(\sup\{m/n:\;u_1\cdots u_m=v_1\cdots v_n\), where \(u_i,v_j\) are irreducible\(\}\), in the case when \(R_0\) is not a field.
scientific article; zbMATH DE number 1997874