On the multiplicative monoid of n × n matrices over Zpm

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For any positive integers m, n and a prime number p, we introduce the concept of invariant factors for matrices over Zpm first, then investigate Green's relations, Green's relation equivalence classes, Schützenberger groups of D-classes, group H-classes and regular principal factors of the matrix multiplicative monoid Mn (Zpm). As corollaries, we characterize a matrix which has a group inverse in Mn (Zpm). © 2007 Elsevier B.V. All rights reserved.




Cao, Y. (2007). On the multiplicative monoid of n × n matrices over Zpm. Discrete Mathematics, 307(24), 3081–3096. https://doi.org/10.1016/j.disc.2007.03.021

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