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| Zero element (disambiguation) ： ウィキペディア英語版 |
Zero element
In mathematics, a zero element is one of several generalizations of the number zero to other algebraic structures. These alternate meanings may or may not reduce to the same thing, depending on the context.
==Additive identities==
An additive identity is the identity element in an additive group. It generalises the property . Examples include:
* The zero vector under vector addition
* The zero function or zero map defined by under pointwise addition , since
* The empty set under set union
* An empty sum or empty coproduct
* An initial object in a category (an empty coproduct, and so an identity under coproducts)
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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