additive identity

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun An element that in a given mathematical system leaves unchanged any element to which it is added.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun algebra An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally denoted +). That is, x + 0 = 0 + x = x for any x in the structure.