Zero element

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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:

• An additive identity, i.e., the identity element in an additive group
• An absorbing element in a multiplicative semigroup or semiring
• A least element in a partially ordered set
• The distinguished element 0 in a field or ring, which is the additive identity and the multiplicative absorbing element, and whose principal ideal is the smallest ideal

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