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I am studying about ideals of spatial (minimal) tensor product of $C^{\ast}$-algebras but I did not find any book/paper in which all the results are given.

What are some results or folklore which are well known about the ideals(primitive/prime/modular) of spatial tensor products of $C^{\ast}$-algebras.

To start with, if $A$ or $B$ is exact then closed ideals of spatial tensor product $A \otimes B$ are generated by tensor product of two sided closed ideals.

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Well, one source I know which "considers ideals of tensor products of $C^*$-algebras" is David McConnell's thesis: $C_0(X)$-structure in $C^*$-algebras, multiplier algebras and tensor products.

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  • $\begingroup$ Thank you Matthew, I will have a look. $\endgroup$
    – Math Lover
    Commented Jun 12, 2020 at 8:55
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You can also find some results of that flavor in Closed ideals and Lie ideals of minimal tensor product of certain C*-algebras .

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