Star operations and pullbacks

In this paper we study the star operations on a pullback of integral domains. In particular, we characterize the star operations of a domain arising from a pullback of “a general type” by introducing new techniques for “projecting” and “lifting” star operations under surjective homomorphisms of integral domains. We study the transfer in a pullback (or with respect to a surjective homomorphism) of some relevant classes or distinguished properties of star operations such as v−, t−, w−, b−, d−, finite type, e.a.b., stable, and spectral operations. We apply part of the theory developed here to give a complete positive answer to a problem posed by D.F. Anderson in 1992 concerning the star operations on the “D+M” constructions.