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Kähler differential
In mathematics, Kähler differentials provide an adaptation of differential forms to arbitrary commutative rings or schemes.
==Presentation==
The idea was introduced by Erich Kähler in the 1930s. It was adopted as standard, in commutative algebra and algebraic geometry, somewhat later, following the need to adapt methods from geometry over the complex numbers, and the free use of calculus methods, to contexts where such methods are not available.
Let ''R'' and ''S'' be commutative rings and ''φ'':''R'' → ''S'' a ring homomorphism. An important example is for ''R'' a field and ''S'' a unital algebra over ''R'' (such as the coordinate ring of an affine variety).
An ''R''-linear derivation on ''S'' is a map to an ''S''-module ''M'' with ''R'' in its kernel, satisfying Leibniz rule . The module of Kähler differentials is defined as the ''R''-linear derivation that factors all others.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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