Regular modules

David J. Fieldhouse
1972 Proceedings of the American Mathematical Society  
Pierce [3] has shown that over a commutative regular ring every finitely generated submodule of an »»-generated module is «-generated, and then has asked if this result holds for noncommutative regular rings. Here the result is shown for regular modules over any associative ring, which answers Pierce's question since a ring is regular if and only if every module is regular.
doi:10.1090/s0002-9939-1972-0292882-4 fatcat:hzzqee76bbcbrejn6y5crfk2pm