An interleaved execution of transactions in a database system is serializable if the effect of the execution is equivalent to that of some serial execution of the transactions. Several notions of serializability have been defined in the literature. They differ with respect to whether the effect is equivalent regarding the values read by the transactions or the final database state, that is, the values read by the fictitious final transaction. We introduce a generalized notion called S- serializability, where the subset S of transactions read the same values as in some serial execution. We also introduce C-serializability where the final values for the subset C of data items are the same as in some serial execution. By combining these two notions, we get \((S+C)\)- serializability. We give simple and intuitive characterizations for all these notions of serializability.