We consider the problem of the translation of view updates to database updates. Our research uses an algebraic approach in order to classify different properties of views with respect to the treatment of updates. In our classification, special attention is paid to a class of views that we call "consistent". Informally speaking, a consistent view is a view with the following property: if the effect of a view update program on a view state is determined, then the corresponding database update is unambiguously determined. Thus, in order to know how to translate a given view update into a database update, it is not necessary to know the sequence of particular operations of the view update program; it is sufficient to be aware of a functional specification of such a program. We show how conditional updates can be modeled and prove that consistent views have a number of interesting properties with respect to the concurrency of update transactions. Moreover, we show that the class of consistent views includes, as a particular subset, the class of views which translate updates under maintenance of a constant complement. However, we give examples of important realistic views that are consistent but do not translate updates under constant complement. The results of Bancillion and Spyratos [ACM-TODS 6:4, 1981] are generalized in order to capture the update semantics of the entire class of consistent views.