# Zero element

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In algebra, the term **zero element** is used with two meanings,
both in analogy to the number zero.

- For an additively written binary operation,
*z*is a*zero element*if (for all*g*)

*z*+*g*=*g*=*g*+*z*

- i.e., it is the (unique) neutral element for this operation.

- For a multiplicatively written binary operation,
*a*is a*zero element*if (for all*g*)

*ag*=*g*=*ga*

- i.e., it is the (unique) absorbing element for this operation.

In rings (not only the real or complex numbers) 0 is the zero element in both senses.

In addition to these "two-sided" zero elements, (one-sided) *left* or *right* zero elements are also considered
for which only one of the two identities is valid for all *g*.

One-sided zero elements need not be unique.