Absorbing element

In algebra, an absorbing element or a zero element for a binary operation has a property similar to that of multiplication by zero.

Formally, let be a binary operation on a set X. An element O of X is absorbing for if

holds for all x in X. An absorbing element, if it exists, is unique.

[edit] Examples

• The zero (additive identity element) of a ring is an absorbing element for the ring multiplication.
• The zero matrix is the absorbing element for matrix multiplication.
• The empty set is the absorbing element for intersection of sets.

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