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# canonical localizing system

###### Definition 0.1.

Let $R$ be a ring. The *canonical localizing system* $S_{{cl}}$ on $R$
is defined as the strongest localizing system $F$ on $R$, such that $R$ is $F$-closed.

Note that there is a localizing subcategory $\mathcal{F}$ that contains all strongest localizing systems $F$.

Defines:

localizing subcategory

Keywords:

canonical localizing system

Type of Math Object:

Definition

Major Section:

Reference

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## Mathematics Subject Classification

18-00*no label found*18E05

*no label found*

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