Geodesic
Indices of imprimitivity of the temporal components of a semigroup of nonnegative matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 17-30 
Yu. A. Al'pin; V. S. Al'pina. Indices of imprimitivity of the temporal components of a semigroup of nonnegative matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 17-30. http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a1/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is proved that the index of imprimitivity of a semigroup of nonnegative block-monominal matrices free of zero rows decomposes into a sum of the indices of imprimitivity of its temporal components, and if the semigroup is block irreducible, then the indices of imprimitivity of all the temporal components are equal.

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