Star operations and Pullbacks

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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.