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YCor
YCor
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Primitive Idealsideals of Inductive Limitsinductive limits of $C^*$-algebras

I am trying to understand ideals of direct limits in the category of $C^{\ast}$-algebras.

Let $(A_n,f_n)$ be a direct sequence of $C^{\ast}$-algebras and let $I$ be a Primitiveprimitive (modular)ideal ideal of direct limit $\varinjlim A_n $. Is it true that there exists Primitiveprimitive (modular) ideals $I_i$ of $A_i$ such that $I= \varinjlim I_i$?

Unfortunately I could not find any reference.Any reference or ideas?

Primitive Ideals of Inductive Limits

I am trying to understand ideals of direct limits in the category of $C^{\ast}$-algebras.

Let $(A_n,f_n)$ be a direct sequence of $C^{\ast}$-algebras and let $I$ be a Primitive(modular)ideal of direct limit $\varinjlim A_n $. Is it true that there exists Primitive(modular) ideals $I_i$ of $A_i$ such that $I= \varinjlim I_i$

Unfortunately I could not find any reference.Any reference or ideas?

Primitive ideals of inductive limits of $C^*$-algebras

I am trying to understand ideals of direct limits in the category of $C^{\ast}$-algebras.

Let $(A_n,f_n)$ be a direct sequence of $C^{\ast}$-algebras and let $I$ be a primitive (modular) ideal of direct limit $\varinjlim A_n $. Is it true that there exists primitive (modular) ideals $I_i$ of $A_i$ such that $I= \varinjlim I_i$?

Unfortunately I could not find any reference.Any reference or ideas?

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Math Lover
Math Lover
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Primitive Ideals of Inductive Limits

I am trying to understand ideals of direct limits in the category of $C^{\ast}$-algebras.

Let $(A_n,f_n)$ be a direct sequence of $C^{\ast}$-algebras and let $I$ be a Primitive(modular)ideal of direct limit $\varinjlim A_n $. Is it true that there exists Primitive(modular) ideals $I_i$ of $A_i$ such that $I= \varinjlim I_i$

Unfortunately I could not find any reference.Any reference or ideas?