identity vs identity element

identity and identity element both are nouns.

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

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

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

Other synonyms of identity include identity operator.

identity (noun)	identity element (noun)
the distinct personality of an individual regarded as a persisting entity	an operator that leaves unchanged the element on which it operates
exact sameness
the individual characteristics by which a thing or person is recognized or known
an operator that leaves unchanged the element on which it operates