Abstract. The authors analyze the problem of the invariance of keys, including simple keys, with respect to operations of table algebras, a modern analog of classical relational Codd’s algebras. It is shown that the keys are invariant with respect to operations of intersection, difference, selection, join, and division, but for simple keys invariance does not hold. It is shown that keys, including simple keys, are invariant with respect to the operation of renaming. The necessary and sufficient conditions under which the keys, including simple keys, are invariant with respect to operations of projection and active supplement are established. The results of the study are of theoretical and practical interest and can be used to choose optimal keys in design of relational databases.

Keywords: database, table algebra, key.