Geodesic
Some Criteria for Hermite Rings and Elementary Divisor Rings
Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1380-1383

Voir la notice de l'article provenant de la source Cambridge University Press

Recall that a ring R (all rings considered are commutative with unit) is an elementary divisor ring (respectively, a Hermite ring) provided every matrix over R is equivalent to a diagonal matrix (respectively, a triangular matrix). Thus, every elementary divisor ring is Hermite, and it is easily seen that a Hermite ring is Bezout, that is, finitely generated ideals are principal. Examples have been given [4] to show that neither implication is reversible. 
Shores, Thomas S.; Wiegand, Roger. Some Criteria for Hermite Rings and Elementary Divisor Rings. Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1380-1383. doi: 10.4153/CJM-1974-131-8
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