A commutative ring S with identity element 1 is called an elementary divisor ring (resp. Hermite ring) if for every matrix A over S there exist nonsingular matrices P, Q such that PAQ (resp. AQ) is a diagonal matrix (resp. triangular matrix). It is clear that every elementary divisor ring is an Hermite ring, and that every Hermite ring is an F-ring (that is, a commutative ring with identity in which all finitely generated ideals are principal).
© 1955 University of Michigan
Henriksen, Melvin. "Some remarks on elementary divisor rings II." Michigan Mathematical Journal 3.2 (1955): 159-163. DOI: 10.1307/mmj/1028990029