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Ideal sheaf
In algebraic geometry and other areas of mathematics, an ideal sheaf (or sheaf of ideals) is the global analogue of an ideal in a ring. The ideal sheaves on a geometric object are closely connected to its subspaces. == Definition ==
Let ''X'' be a topological space and ''A'' a sheaf of rings on ''X''. (In other words, (''X'', ''A'') is a ringed space.) An ideal sheaf ''J'' in ''A'' is a subobject of ''A'' in the category of sheaves of ''A''-modules, i.e., a subsheaf of ''A'' viewed as a sheaf of abelian groups such that : Γ(''U'', ''A'') · Γ(''U'', ''J'') ⊆ Γ(''U'', ''J'') for all open subsets ''U'' of ''X''. In other words, ''J'' is the sheaf of ''A''-submodules of ''A''.
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