Global dimension
= Global dimension
{title2=$\operatorname{gldim}R=\sup_M\operatorname{pd}_RM$}
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= Global homological dimension
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The global dimension of a <ring> is the supremum of the <projective dimensions> of all its <modules>, allowing infinity. It measures the longest <projective resolution> needed by any <module>. For a <field> it is zero, since every <module> is a <vector space> and hence free.