References: The multiplicativity of the smith normal form ∗

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MacDuffee , C.C. 1946 . The Theory of Matrices Chelsea
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Newman , M. 1972 . Integral Matrices , New York : Acad. Press .
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Prokip , V.M. 1991 . About factorisation of polynomial matrix into factors with prescribed characteristic polynomials . Dokl. Acad Nauk of Ukraine SSR. Ser. A , 3 : 20 – 22 .
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Newman , M. 1993 . Multiplicativity of the Smith Normal Form . Linear and Multilinear Algebra , 36 : 223 – 224 .
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The multiplicativity of the smith normal formFootnote^∗
^∗The statement of Theorem 1 ws communicated by V. Prokip to M. Newman on April 17, 1993 and was reported in [4]

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The multiplicativity of the smith normal formFootnote∗∗The statement of Theorem 1 ws communicated by V. Prokip to M. Newman on April 17, 1993 and was reported in [4]

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The multiplicativity of the smith normal formFootnote^∗
^∗The statement of Theorem 1 ws communicated by V. Prokip to M. Newman on April 17, 1993 and was reported in [4]