Geodesic
On the one-side equivalence of matrices with given canonical diagonal form
Algebra and discrete mathematics, Tome 12 (2011) no. 2, pp. 102-111.

Voir la notice de l'article provenant de la source Math-Net.Ru

The simpler form of a matrix with canonical diagonal form $\mathrm{diag}(1,\dots,1,\varphi,\dots,\varphi)$ obtained by the one-side transformation is determined.
Keywords: adequate ring, canonical diagonal form, Hermite normal form
Mots-clés : one-side equivalence of matrices, invariants, primitive matrices. 
@article{ADM_2011_12_2_a9,
     author = {V. Shchedryk},
     title = {On the one-side equivalence of matrices with given canonical diagonal form},
     journal = {Algebra and discrete mathematics},
     pages = {102--111},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2011_12_2_a9/}
}
TY  - JOUR
AU  - V. Shchedryk
TI  - On the one-side equivalence of matrices with given canonical diagonal form
JO  - Algebra and discrete mathematics
PY  - 2011
SP  - 102
EP  - 111
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2011_12_2_a9/
LA  - en
ID  - ADM_2011_12_2_a9
ER  - 
%0 Journal Article
%A V. Shchedryk
%T On the one-side equivalence of matrices with given canonical diagonal form
%J Algebra and discrete mathematics
%D 2011
%P 102-111
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2011_12_2_a9/
%G en
%F ADM_2011_12_2_a9
V. Shchedryk. On the one-side equivalence of matrices with given canonical diagonal form. Algebra and discrete mathematics, Tome 12 (2011) no. 2, pp. 102-111. http://geodesic.mathdoc.fr/item/ADM_2011_12_2_a9/

[1] Helmer O., “The elementary divisor theorem for certain rings without chain condition”, Bull. Amer. Math. Soc., 49 (1943), 225–236 | DOI | MR | Zbl

[2] Shchedryk V.P., “Structure and properties of matrix divisors over commutative elementary divisor domain”, Math. studii, 10:2 (1998), 115–120 | MR | Zbl

[3] Kazimirskij P.S., Decomposition of matrix polynomials into factors, Naukova dumka, Kyiv, 1981, 224 pp.

[4] Bhowmik G., Ramare O., “Algebra of matrix arithmetic”, Journal of Algebra, 210 (1998), 194–215 | DOI | MR | Zbl

[5] Shchedryk V.P., “Some determinant properties of primitive matrices over Bezout B- domain”, Algebra and Discrete Mathematics, 2005, no. 2, 46–57 | MR | Zbl