disagree vs disagreement

disagree is not a noun while disagreement is a noun.

Word	Noun	Adjective	Verb	Adverb
disagree	No	No	Yes	No
disagreement	Yes	No	No	No

disagree (noun)	disagreement (noun)
	a difference between conflicting facts or claims or opinions
	the speech act of disagreeing or arguing or disputing
	a conflict of people's opinions or actions or characters

disagree (verb)	disagreement (verb)
be of different opinions
be different from one another