identity element vs identity

identity element and identity both are nouns.

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

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

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

Other synonyms of identity element include identity operator.

identity element (noun)	identity (noun)
an operator that leaves unchanged the element on which it operates	the distinct personality of an individual regarded as a persisting entity
	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