Elasticity of A + XB[ X] domains

Abstract

Let A ⊂ B be an extension of integral domains and X be an indeterminate over B. In this paper, we study the elasticity of atomic domains of the form A + XB[ X]. We pay particular attention to when such domains are half-factorial domains, and in particular, we answer a question raised by V. Barucci et al. Finally, we investigate the elasticity of Z[√d] + X Z[ (1 + √d) 2 ][X] , where d is a nonzero square-free integer, d  1 ( mod 4). This provides an example such that A + XB[ X] is a HFD where A and B are HFDs but not UFDs.