The Derived Sequence of a Pre-Jaffard Family

Abstract We introduce the concept of pre-Jaffard family , a generalization Jaffard families obtained by substituting locally finite hypothesis with much weaker compactness hypothesis. From any such family, we construct sequence overrings starting domain that allows to decompose stable semistar operations and singular length functions in more cases than what is allowed families. also apply one-dimensional domains, unifying treatment sharp dull degree Prüfer domain.