An e such that for all x∈S, e*x=x*e=x

(chk) ∀a, ∃e such that a*e = e*a = a를 만족하는. 이 때 e가 항등원.

[[덧셈,addition]]의 '''항등원''' = 0 (∵ x+0=0+x=x)
[[곱셈,multiplication]]의 항등원 = 1
...
각각
 [[덧셈항등원,additive_identity]] https://mathworld.wolfram.com/AdditiveIdentity.html
  덧셈에 대한 항등원?
  [[덧셈,addition]]
  보통 [[영,zero]]
  [[체,field]]의 조건 중 하나?
  https://en.wiktionary.org/wiki/additive_identity#English
  https://en.wikipedia.org/wiki/Additive_identity
 [[곱셈항등원,multiplicative_identity]] https://mathworld.wolfram.com/MultiplicativeIdentity.html
  보통 [[하나,one]]
  [[체,field]]의 조건 중 하나?
  [[곱셈,multiplication]]
  https://en.wiktionary.org/wiki/multiplicative_identity#English
맞는지?

[[행렬곱셈,matrix_multiplication]] 의 항등원?은 - chk
[[항등행렬,identity_matrix]] = [[단위행렬,unit_matrix]] ''I'' or ''E''

left identity
left identity element
https://proofwiki.org/wiki/Definition:Left_Identity
right identity
right identity element
https://proofwiki.org/wiki/Definition:Right_Identity
two-sided identity
two-sided identity element
https://proofwiki.org/wiki/Definition:Identity_Element
https://planetmath.org/leftidentityandrightidentity
... Ggl:"left identity right identity"

ADDIDENTITYHERE

----
비교: [[역원,inverse_element]]

AKA 줄여서 '''identity''' (저기엔 [[항등식,identity]]의 뜻도 있음)
AKA '''neutral element'''

mklink
[[항등함수,identity_function]]

Twins:
[[https://terms.naver.com/entry.naver?docId=3338360&cid=47324&categoryId=47324 수학백과: 항등원]]
https://planetmath.org/identityelement - syn. '''neutral element'''
https://en.citizendium.org/wiki/Identity_element
https://encyclopediaofmath.org/wiki/Identity_element - ''neutral element, unit element, zero element''
[[WpEn:Identity_element]]
https://ncatlab.org/nlab/show/identity+element - "sometimes also called '''neutral element'''"
https://groupprops.subwiki.org/wiki/Identity_element

https://everything2.com/title/identity+element
[[WtEn:identity_element]]

// forked from [[항등식,identity]]... 항등- (identity-) 관련으로 분류? see 항등식.

Up: [[대수구조,algebraic_structure]] [[군론,group_theory]]? [[항등성,identity]] [[원소,element]]