The completeness of relational algebra is more of an academic than a practical topic. Among other things, relational algebra has multi-level operations, such as various types of joins, data manipulation operations, grouping, and selection. Therefore, the very concept of completeness is blurred across these levels, in contrast to the operations of binary logic and other operations to which the concept of completeness is applied.

However, I have dedicated a short article to this topic.

Relational Databases — Completeness of Relational Algebra Operations