Today the set-theoretic operations of intersection $\cap$ [German: Durchschnitt] and union $\cup$ [German: Vereinigung] are standard.
The modern notations are present in the first edition of van der Waerden's Moderne Algebra (1930). However, the notation is mostly missing from Steinitz' Algebraische Theorie der Körper (1910), which was a precursor of van der Waerden. Instead of Menge (for set), Steinitz uses System. The term Durchschnitt is present in Steinitz, but the word Vereinigung and the symbols $\cap,\cup$ are missing.
Has anything been written on the history of set-theoretic language in algebra?