On the preservation of keys in the table algebras - Senchenko, A. S. (Reports of the National Academy of Sciences of Ukraine, 2015)
The problem of preservation of keys, including simple keys, by the signature operations of table algebras is investigated. It is shown that the operations of intersection, difference, selection, join, and division of tables preserve the keys and do not preserve the simple keys, whereas the operations of projection and renaming preserve both. The necessary and sufficient conditions, under which the operation of active supplement preserves the key, are found.