User talk:136.49.55.216
The terminology of ``ring of dual numbers" over a field is standard in algebraic geometry, and it is used for instance in Robin Hartshorne's standard textbook Algebraic Geometry, notably in chapter II, exercise 2.8 (page 80). This exercise guides the reader through precisely the interpretation of maps out of Spec k[x]/(x^2) as elements of the tangent space to a scheme, as I described in my proposed addendum to the Wikipedia page. Dual numbers are again referenced in the main body of the textbook, including in Chapter III example 9.13.1, where they are used to describe infinitesimal deformations of a scheme.
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