Elementary Divisor domains and Bézout domains

It is well known that an Elementary Divisor domain R is a Bézout domain, and it is a classical open question to determine whether the converse statement is false. In this article, we provide new chains of implications between R is an Elementary Divisor domain and R is Bézout defined by hyperplane co...

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Bibliographic Details
Published in:Journal of algebra 2012-12, Vol.371, p.609-619
Main Author: Lorenzini, Dino
Format: Article
Language:English
Subjects:
Bézout ring
Elementary Divisor ring
Hermite ring
Rings defined by matrix properties
Symmetric matrix
Trace zero matrix
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Summary:It is well known that an Elementary Divisor domain R is a Bézout domain, and it is a classical open question to determine whether the converse statement is false. In this article, we provide new chains of implications between R is an Elementary Divisor domain and R is Bézout defined by hyperplane conditions in the general linear group. Motivated by these new chains of implications, we construct, given any commutative ring R, new Bézout rings associated with R.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2012.08.020