Indecomposable and irreducible \(t\)-monomial matrices over commutative rings

Vitaliy Mykhaylovych Bondarenko, Maria Bortos, Ruslana Dinis, Alexander Tylyshchak

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

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