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References
N. Jacobson, Theory of Rings [Russian translation], IL, Moscow (1947).
A. N. Alekseichuk, “Limit distribution of the number of solutions of a system of random linear homogeneous equations with a uniform coefficient matrix over a finite local ring,” Kibemetika i Sistemnyi Analiz, No. 3, 166-171 (1998).
A. A. Nechaev, “Finite rings of principal ideals,” Mat. Sb.,91, No. 3, 350–366 (1973).
L. E. Fuller, “A canonical set of matrices over a principal ideal ring modulo pn,” Can. J. Math.,7, 54–59 (1955).
B. R. McDonald, “Enumeration of canonical matrices under row equivalence over a principal ideal domain modulo pn,” Duke Math. J.,3, 393–402 (1970).
V. N. Sachkov, An Introduction to Combinatorial Methods of Discrete Mathematics [in Russian], Nauka, Moscow (1982).
G. Andrews, Partition Theory [in Russian], Nauka, Moscow (1982).
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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 112–118, September–October, 1998.
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Alekseichuk, A.N. Limit distributions of the length and rank of a module generated by the columns of a random equiprobable matrix over a finite chain ring. Cybern Syst Anal 34, 726–731 (1998). https://doi.org/10.1007/BF02667046
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DOI: https://doi.org/10.1007/BF02667046