identity operator vs identity element

identity operator and identity element both are nouns.

Word	Noun	Adjective	Verb	Adverb
identity operator	Yes	No	No	No
identity element	Yes	No	No	No

As nouns, identity operator and identity element are synonyms defined as:

identity operator and identity element: an operator that leaves unchanged the element on which it operates

Other synonyms of identity operator include identity.

identity operator (noun)	identity element (noun)
an operator that leaves unchanged the element on which it operates	an operator that leaves unchanged the element on which it operates