Complex sentence: Noncommutative algebra is the study of results applying to rings that are not required to be commutative; however, many important results in this area apply to commutative rings as special cases.
Split into simpler sentences: Noncommutative algebra is the study of results applying to rings that are not required to be commutative. Many important results in the field of noncommutative algebra area apply to commutative rings as special cases.