On the star class group of a pullback

Abstract: For the domain R arising from the construction T, M, D, we relate the star class groups of R to those of T and D. More precisely, let T be an integral domain, M a nonzero maximal ideal of T, D a proper subring of , the natural projection, and let . For each star operation * on R, we define the star operation on D, i.e., the “projection” of * under φ, and the star operation on T, i.e., the “extension” of * to T. Then we show that, under a mild hypothesis on the group of units of T, if * is a star operation of finite type, then the sequence of canonical homomorphisms is split exact. In particular, when , we deduce that the sequence is split exact. The relation between and (and between and ) is also investigated. [Copyright &y& Elsevier]