#### Document Type

Article

#### Department

Mathematics (HMC)

#### Publication Date

1955

#### Abstract

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).

#### Rights Information

© 1955 University of Michigan

#### Terms of Use & License Information

#### DOI

10.1307/mmj/1028990029

#### Recommended Citation

Henriksen, Melvin. "Some remarks on elementary divisor rings II." Michigan Mathematical Journal 3.2 (1955): 159-163. DOI: 10.1307/mmj/1028990029

## Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,476.

Publisher pdf, posted with permission.

Published by the University of Michigan Department of Mathematics.