Systems of linear equations over modules
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 4, pp. 979-991.

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Some necessary conditions for solvability of linear equation systems over modules are studied. In some situations these conditions are also sufficient.
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V. P. Elizarov. Systems of linear equations over modules. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 4, pp. 979-991. http://geodesic.mathdoc.fr/item/FPM_2002_8_4_a2/

[1] Elizarov V. P., “Sistemy lineinykh uravnenii nad kommutativnym koltsom”, Uspekhi mat. nauk, 48:2 (1993), 181–182 | MR | Zbl

[2] Elizarov V. P., “Sistemy lineinykh uravnenii nad kvazifrobeniusovymi koltsami”, Fundam. i prikl. mat., 1:2 (1995), 535–539 | MR | Zbl

[3] Elizarov V. P., “Usloviya sovmestnosti sistem lineinykh uravnenii nad koltsami”, Fundam. i prikl. mat., 6:3 (2000), 777–788 | MR | Zbl

[4] Malashonok G. I., Sistema lineinykh uravnenii v kommutativnom koltse, Kievskii gosudarstvennyi universitet, 1986

[5] Nechaev A. A., “Konechnye kvazifrobeniusovy moduli, prilozheniya k kodam i lineinym rekurrentam”, Fundam. i prikl. mat., 1:1 (1995), 229–254 | MR | Zbl

[6] Rodosskii K. A., Algoritm Evklida, Nauka, M., 1988 | MR | Zbl

[7] Camion P., Levy L. S., Mann H. B., “Linear equations over a commutative ring”, J. Algebra, 17:3 (1971), 432–441 | DOI | MR

[8] Ching W.-S., “Linear equations over commutative rings”, Linear Algebra and Appl., 18:3 (1977), 257–266 | DOI | MR | Zbl

[9] Hermida J. A., Sanchez-Giralda T., “Linear equations over commutative rings and determinantal ideals”, J. Algebra, 99:1 (1986), 72–79 | DOI | MR | Zbl

[10] Kaplansky I., “Elementary divisors and modules”, Trans. Amer. Math. Soc., 66 (1949), 464–491 | DOI | MR | Zbl

[11] Kertesz A., “The general theory of linear equation systems over semisimple rings”, Publ. Math. Debrecen, 4:1–2 (1955), 79–86 | MR | Zbl

[12] Kertesz A., “Systems of equations over modules”, Acta Scient. Math. Szeged, 18:3–4 (1957), 207–234 | MR | Zbl

[13] Kuhn H. W., “Solvability and consistency for linear equations and inequalities”, Amer. Math. Monthly, 63:4 (1956), 217–232 | DOI | MR | Zbl

[14] Smith H. J. S., “On systems of linear indeterminate equations and congruences”, Phil. Trans. Royal Soc. London, A151 (1861), 293–326 | DOI

[15] Smith H. J. S., “On the arithmetical invariants of a rectangular matrix of which the constituents are integral numbers”, Proc. London Math. Soc., 4 (1873), 236–249 | DOI

[16] Steinitz E., “Rechteckige Systeme und Moduln in algebraischen Zahlkorpern, I”, Math. Ann., 71:3 (1912), 328–354 | DOI | MR | Zbl

[17] Van der Waerden B. L., Moderne Algebra, V. 2, Springer, Berlin, 1931