Elementary divisor domain

Origin
The notion of an elementary divisor domain was introduced by Kaplansky in his paper Elementary Divisors and Modules.

It was later generalized to elementary divisor ring by Gillman and Henriksen, in Some remarks about elementary divisor rings.

Symbol-free definition
An elementary divisor domain or Hermite domain is any of the following equivalent things:


 * An integral domain which is also an elementary divisor ring
 * An integral domain which is also a Hermite ring

Stronger properties

 * Principal ideal domain