The inheritance of tracial nuclear dimension for centrally large subalgebras

In this paper, we focus on the inheritance of certain types of tracial nuclear dimension for centrally large subalgebras. Let A be an infinite dimensional simple unital C*-algebra and B be a centrally large subalgebra of A. Suppose that A or B is nuclear. We prove A has certain types of tracial nuclear dimension no more than n if B has the same types of tracial nuclear dimension no more than n.