Geodesic
Indecomposable and irreducible $t$-monomial matrices over commutative rings
Algebra and discrete mathematics, Tome 22 (2016) no. 1, pp. 11-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We introduce the notion of the defining sequence of a permutation indecomposable monomial matrix over a commutative ring and obtain necessary conditions for such matrices to be indecomposable or irreducible in terms of this sequence.
Keywords: local ring, similarity, irreducible matrix, canonically $t$-cyclic matrix, defining sequence, representation.
Mots-clés : indecomposable matrix, group 
@article{ADM_2016_22_1_a1,
     author = {Vitaliy M. Bondarenko and Maria Yu. Bortos and Ruslana F. Dinis and Alexander A. Tylyshchak},
     title = {Indecomposable and irreducible $t$-monomial~matrices over commutative rings},
     journal = {Algebra and discrete mathematics},
     pages = {11--20},
     year = {2016},
     volume = {22},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a1/}
}
TY  - JOUR
AU  - Vitaliy M. Bondarenko
AU  - Maria Yu. Bortos
AU  - Ruslana F. Dinis
AU  - Alexander A. Tylyshchak
TI  - Indecomposable and irreducible $t$-monomial matrices over commutative rings
JO  - Algebra and discrete mathematics
PY  - 2016
SP  - 11
EP  - 20
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a1/
LA  - en
ID  - ADM_2016_22_1_a1
ER  - 
%0 Journal Article
%A Vitaliy M. Bondarenko
%A Maria Yu. Bortos
%A Ruslana F. Dinis
%A Alexander A. Tylyshchak
%T Indecomposable and irreducible $t$-monomial matrices over commutative rings
%J Algebra and discrete mathematics
%D 2016
%P 11-20
%V 22
%N 1
%U http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a1/
%G en
%F ADM_2016_22_1_a1
Vitaliy M. Bondarenko; Maria Yu. Bortos; Ruslana F. Dinis; Alexander A. Tylyshchak. Indecomposable and irreducible $t$-monomial matrices over commutative rings. Algebra and discrete mathematics, Tome 22 (2016) no. 1, pp. 11-20. http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a1/

[1] V. M. Bondarenko, M. Yu. Bortos, M. Yu. Dinis, A. A. Tylyshchak, “Reducibility and irreducibility of monomial matrices over commutative rings”, Algebra Discrete Math., 16:2 (2013), 171–187 | MR | Zbl

[2] F. R. Gantmaher, The theory of matrices, FIZMATLIT, 2004, 560 pp.

[3] R. A. Horn, C. R. Johnson, Matrix Analysis, 2nd ed., Cambridge University Press, Cambridge, 2013, 643 pp. | MR | Zbl

[4] P. M. Gudivok, I. B. Chukhraj, “On the number of indecomposable matrix representations of given degree of a finite $p$-group over commutative local rings of characteristic $p^s$”, Nauk. Visn. Uzhgorod Univ. Ser. Mat. Inform., 5 (2000), 33–40 (Ukrainian) | Zbl