Field: Difference between revisions
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The word "field" has two unrelated meanings in mathematics. In algebra, it refers to a nontrivial commutative ring in which every nonzero element is a unit, while in differential geometry and theoretical physics, it refers to a function from a manifold to a vector space. This ambiguity does not exist in some languages like french and german, where fields in the former sense are referred to as "bodies" (french: corps, german: Körper). | The word "field" has two unrelated meanings in mathematics. In algebra, it refers to a nontrivial commutative ring in which every nonzero element is a unit, while in differential geometry and theoretical physics, it refers to a function from a manifold to a vector space. This ambiguity does not exist in some languages like french and german, where fields in the former sense are referred to as "bodies" (french: corps, german: Körper). | ||
Latest revision as of 14:55, 21 October 2022
The word "field" has two unrelated meanings in mathematics. In algebra, it refers to a nontrivial commutative ring in which every nonzero element is a unit, while in differential geometry and theoretical physics, it refers to a function from a manifold to a vector space. This ambiguity does not exist in some languages like french and german, where fields in the former sense are referred to as "bodies" (french: corps, german: Körper).
