scholarly journals Bézout domains and lattice-valued modules

2020 ◽  
Vol 224 (1) ◽  
pp. 444-467 ◽  
Author(s):  
Sonia L'Innocente ◽  
Françoise Point
Keyword(s):  
Bezout Domains

Bezout domains and skew polynomials

2000 ◽  
Vol 55 (5) ◽  
pp. 1005-1006 ◽  
Author(s):  
A A Tuganbaev
Keyword(s):  
Skew Polynomials ◽  
Bezout Domains

Elementary matrix reduction over Bézout domains

2019 ◽  
Vol 18 (08) ◽  
pp. 1950141
Author(s):  
Huanyin Chen ◽  
Marjan Sheibani Abdolyousefi
Keyword(s):  
Elementary Divisor ◽  
Bezout Domain ◽  
Elementary Matrix ◽  
Matrix Reduction ◽  
Elementary Divisor Ring ◽  
Bezout Domains ◽  
Diagonal Reduction

A ring [Formula: see text] is an elementary divisor ring if every matrix over [Formula: see text] admits a diagonal reduction. If [Formula: see text] is an elementary divisor domain, we prove that [Formula: see text] is a Bézout duo-domain if and only if for any [Formula: see text], [Formula: see text] such that [Formula: see text]. We explore certain stable-like conditions on a Bézout domain under which it is an elementary divisor ring. Many known results are thereby generalized to much wider class of rings.

scholarly journals Almost Beźout Domains .II.

1994 ◽  
Vol 167 (3) ◽  
pp. 547-556 ◽  
Author(s):  
D.D. Anderson ◽  
K.R. Knopp ◽  
R.L. Lewin
Keyword(s):  
Bezout Domains

On bézout domains, elementary divisor rings, and pole assignability

1984 ◽  
Vol 12 (24) ◽  
pp. 2987-3003 ◽  
Author(s):  
J.W. Brewer ◽  
C. Naudé ◽  
G. Naudé
Keyword(s):  
Elementary Divisor ◽  
Bezout Domains

The monoid rings that are Bezout domains

1981 ◽  
Vol 37 (1) ◽  
pp. 43-47 ◽  
Author(s):  
Pere Menal
Keyword(s):  
Bezout Domains

Overrings of Bezout Domains

1973 ◽  
Vol 16 (4) ◽  
pp. 475-477 ◽  
Author(s):  
Raymond A. Beauregard
Keyword(s):  
Local Ring ◽  
Left Ideal ◽  
Quotient Ring ◽  
Valuation Domain ◽  
Quotient Field ◽  
Bezout Domain ◽  
Ideal Domain ◽  
Chain Conditions ◽  
Bezout Domains

In [2] Brungs shows that every ring T between a principal (right and left) ideal domain R and its quotient field is a quotient ring of R. In this note we obtain similar results without assuming the ascending chain conditions. For a (right and left) Bezout domain R we show that T is a quotient ring of R which is again a Bezout domain; furthermore Tis a valuation domain if and only if T is a local ring.

Geometry of Alternate Matrices over Bezout Domains

2013 ◽  
Vol 20 (02) ◽  
pp. 197-214 ◽  
Author(s):  
Liping Huang ◽  
Yingchun Li ◽  
Kang Zhao
Keyword(s):  
Bezout Domain ◽  
Bezout Domains

Let R be a commutative Bezout domain. Denote by [Formula: see text] the set of all n × n alternate matrices over R. This paper discusses the adjacency preserving bijective maps in both directions on [Formula: see text], and extends Liu's theorem on the geometry of alternate matrices over a field to the case of a Bezout domain.

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