(Q1143328)

English

chain complex

in homological algebra, a structure consisting of a sequence of modules and a sequence of homomorphisms between consecutive modules such that the image of each homomorphism is included in the kernel of the next

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Chain map.svg
400 × 105; 32 KB

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studied in

homological algebra

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discoverer or inventor

Walther Mayer

point in time

1929

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stated in

History of Homological Algebra

defining formula

{\begin{aligned}&\dotsb \xleftarrow {\partial _{0}} A_{0}\xleftarrow {\partial _{1}} A_{1}\xleftarrow {\partial _{2}} A_{2}\xleftarrow {\partial _{3}} \dotsb \\&\partial _{i}\circ \partial _{i+1}=0\end{aligned}}

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in defining formula

\partial _{i}

symbol represents

boundary operator

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i

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maintained by WikiProject

WikiProject Mathematics

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has part(s) of the class

chain

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boundary operator

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Commons category

Complexes (algebra)

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Identifiers

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28 October 2013

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Microsoft Academic ID

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Definition:Chain_Complex

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commonswiki Category:Complexes (algebra)