Sentence:  Two important functions in <WSD>nonassociative</WSD> ring theory are the "commutator" and "associator" which, for elements "a, b, c" in a ring are defined respectively by / ::: ["a, b"] = "ab" − "ba" / and / ::: ["a, b, c"] = "a"("bc") − ("ab")"c". 
Meaning of the word marked with <WSD> tags:  Whose multiplication operation is not assumed to be associative for all elements.