locally free

A sheaf of $\\mathcal{O}_{X}$ -modules $\\mathcal{F}$ on a ringed space $X$ is called locally free if for each point $p\\in X$ , there is an open neighborhood (http://planetmath.org/Neighborhood) $U$ of $x$ such that $\\mathcal{F}|_{U}$ is free (http://planetmath.org/FreeModule) as an $\\mathcal{O}_{X}|_{U}$ -module, or equivalently, $\\mathcal{F}_{p}$ , the stalk of $\\mathcal{F}$ at $p$ , is free as a $(\\mathcal{O}_{X})_{p}$ -module. If $\\mathcal{F}_{p}$ is of finite rank (http://planetmath.org/ModuleOfFiniteRank) $n$ , then $\\mathcal{F}$ is said to be of rank $n$ .

单词	LocallyFree
释义	locally free A sheaf of $\\mathcal{O}_{X}$ -modules $\\mathcal{F}$ on a ringed space $X$ is called locally free if for each point $p\\in X$ , there is an open neighborhood (http://planetmath.org/Neighborhood) $U$ of $x$ such that $\\mathcal{F}\|_{U}$ is free (http://planetmath.org/FreeModule) as an $\\mathcal{O}_{X}\|_{U}$ -module, or equivalently, $\\mathcal{F}_{p}$ , the stalk of $\\mathcal{F}$ at $p$ , is free as a $(\\mathcal{O}_{X})_{p}$ -module. If $\\mathcal{F}_{p}$ is of finite rank (http://planetmath.org/ModuleOfFiniteRank) $n$ , then $\\mathcal{F}$ is said to be of rank $n$ .
随便看	NoetherianModule Noetherian module NoetherianRing noetherian ring NoetherianTopologicalSpace Noetherian topological space NoetherNormalizationLemma Noether normalization lemma NonabelianGroup nonabelian group Nonahedron nonahedron NonassociativeAlgebra non-associative algebra NoncentralChisquaredRandomVariable non-central chi-squared random variable NoncommutativeDynamicModelingDiagrams non-commutative dynamic modeling diagrams NoncommutativeGeometry noncommutative geometry NoncommutativeRingsOfOrderFour non-commutative rings of order four NoncommutativeStructure non-commutative structure NoncommutativeTopology