Abstract: Without the separability condition for C*-algebras, based on the definition of tracial approximate divisibility, and by employing the structural properties of centrally large subalgebras, we prove that tracial approximate divisibility is hereditary with respect to centrally large subalgebras. Let A be an infinite dimensional unital simple C*-algebra and B be a centrally large subalgebra of A. If B has tracial approximate divisibility, then A also has tracial approximate divisibility.

Key words: tracial approximate divisibility, C*-algebra, large subalgebra, centrally large subalgebra