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Some Criteria for Hermite Rings and Elementary Divisor Rings

Published online by Cambridge University Press:  20 November 2018

Thomas S. Shores  and
Roger Wiegand
Thomas S. Shores
Affiliation:
University of Nebraska-Lincoln, Lincoln, Nebraska
Roger Wiegand
Affiliation:
University of Nebraska-Lincoln, Lincoln, Nebraska
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1380 - 1383
Copyright
Copyright © Canadian Mathematical Society 1974

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