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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 10th 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexgave the statement that _[[derivations of smooth functions are vector fields]]_ a dedicated entry of its own, in order to be able to convieniently point to it

   gave the statement that derivations of smooth functions are vector fields a dedicated entry of its own, in order to be able to convieniently point to it

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeMar 10th 2015
   • (edited Mar 10th 2015)
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   Author: Todd_Trimble
   Format: MarkdownItexTaking after this style of entry, I decided to write [[epimorphisms of groups are surjective]]. Added a little on splittings of exact sequences to [[split idempotent]], and to [[derivation]] (mentioning the notion of a derivation of a group valued in a module over that group, a la group cohomology, as a special case of derivations valued in bimodules).

   Taking after this style of entry, I decided to write epimorphisms of groups are surjective. Added a little on splittings of exact sequences to split idempotent, and to derivation (mentioning the notion of a derivation of a group valued in a module over that group, a la group cohomology, as a special case of derivations valued in bimodules).

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 5th 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have expanded the Idea-section and typed up a detailed proof at _[[derivations of smooth functions are vector fields]]_.

   I have expanded the Idea-section and typed up a detailed proof at derivations of smooth functions are vector fields.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeApr 4th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to the reference that Dmitri kindly provided over at *[[tangent bundle]]*: * [[W. F. Newns]], [[A. G. Walker]], _Tangent Planes To a Differentiable Manifold_. Journal of the London Mathematical Society s1-31:4 (1956), 400–407 ([doi:10.1112/jlms/s1-31.4.400](https://doi.org/10.1112/jlms/s1-31.4.400)) <a href="https://ncatlab.org/nlab/revision/diff/derivations+of+smooth+functions+are+vector+fields/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/derivations+of+smooth+functions+are+vector+fields/12">v12</a>, <a href="https://ncatlab.org/nlab/show/derivations+of+smooth+functions+are+vector+fields">current</a>

   added pointer to the reference that Dmitri kindly provided over at tangent bundle:

   • W. F. Newns, A. G. Walker, Tangent Planes To a Differentiable Manifold. Journal of the London Mathematical Society s1-31:4 (1956), 400–407 (doi:10.1112/jlms/s1-31.4.400)

   diff, v12, current

5. • CommentRowNumber5.
   • CommentAuthorDmitri Pavlov
   • CommentTimeFeb 6th 2025
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   Author: Dmitri Pavlov
   Format: MarkdownItexAdded: The case of analytic manifolds is discussed in * [[Claude Chevalley]], Theory of Lie Groups I (Princeton, 1946). The case of $C^\infty$-manifolds is discussed in Section 4 of * Harley Flanders. Development of an extended exterior differential calculus. Transactions of the American Mathematical Society 75:2 (1953), 311-326. [doi](https://doi.org/10.1090/s0002-9947-1953-0057005-8). <a href="https://ncatlab.org/nlab/revision/diff/derivations+of+smooth+functions+are+vector+fields/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/derivations+of+smooth+functions+are+vector+fields/16">v16</a>, <a href="https://ncatlab.org/nlab/show/derivations+of+smooth+functions+are+vector+fields">current</a>

   Added:

   The case of analytic manifolds is discussed in

   • Claude Chevalley, Theory of Lie Groups I (Princeton, 1946).

   The case of $C^\infty$-manifolds is discussed in Section 4 of

   • Harley Flanders. Development of an extended exterior differential calculus. Transactions of the American Mathematical Society 75:2 (1953), 311-326. doi.

   diff, v16, current