Large subalgebra was firstly introduced by Phillips as an abstraction of Putnam subalgebra, which played a critical role on the structure of the C*-algebra of minimal dynamical systems. Then Archey and Phillips gave a stronger concept which is called centrally large subalgebra. An interesting general question consists of considering which properties of (centrally) large subalgebra could be used to deduce properties of the original algebra?

Let $A$ be an infinite dimensional simple unital C*-algebra and let $B$ be a (centrally) large subalgebra of $A$. In this talk, we first show that $A$ has real rank zero if $B$ has real rank zero, without the condition that $B$ has stable rank one. Then we show the permanence about some comparison properties for large subalgebras of a C*-algebra. Last, we give a definition of generalized tracial approximation C*-algebras which generalized the definitions of tracial approximation C*-algebras and large subalgebra.

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