Vitaliy M. Bondarenko, Maria Yu. Bortos, Ruslana F. Dinis, Alexander A. Tylyshchak, “Indecomposable and irreducible <nobr>$t$</nobr>-monomial matrices over commutative rings”, Algebra Discrete Math., 2016, Volume 22, Issue 1,Pages <nobr>11

This article is cited in 2 papers

RESEARCH ARTICLE

Indecomposable and irreducible $t$-monomial matrices over commutative rings

Vitaliy M. Bondarenko^a, Maria Yu. Bortos^a, Ruslana F. Dinis^b, Alexander A. Tylyshchak^c

^a Institute of Mathematics, Tereshchenkivska str., 3, 01601 Kyiv, Ukraine
^b Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko Univ., Volodymyrska str., 64, 01033 Kyiv, Ukraine
^c Faculty of Mathematics, Uzhgorod National Univ., Universytetsyka str., 14, 88000 Uzhgorod, Ukraine

Abstract: 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, indecomposable matrix, irreducible matrix, canonically $t$-cyclic matrix, defining sequence, group, representation.

MSC: 15B33, 15A30

Received: 29.08.2016

Language: English