Elasticity of A + XB[X] domains

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] + XZ[(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.