1. Adams W. W., Loustaunau P., "An introduction to Gröbner bases", American Mathematical Society (1994). 2. Anderson F. W., Fuller K. R., "Rings and Categories of Modules", second ed., Grad. Texts in Math., Vol. 13, Springer-Verlag, Berlin (1992). 3. Brandal W., "Commutative Rings Whose Finitely Generated Modules Decompose", Lecture Notes in Mathematics, 723, Springer, Berlin (1979). 4. Buchberger B., "Ein Algorithms zum Auffinden der Basiselemente des Restklassenrings nach einem nuildimensionalen Polynomideal", PhD thesis, Universität Innsbruck (1965). 5. Conti P., Traverso C., "Buchberger algorithm and integer programming", In Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes AAECC9 (H.F. Mattson, T. Mora, and T.R.N Rao eds.), Lecture Notes in Comput. Sci., Vol. 539, Springer verlag, Berlin and New York (1991) 130-139. 6. Dumas J-G., Giorgi P., Pernet C., "Dense linear Algebra over finite fields: the FFLAS and FFPACK packages", ACM Trans. Math. Softw., Vol. 35, Number 3 (2008)1-35. 7. Dumas J-G., Pernet C., Sultan Z., "Simultaneous computation of the row and column rank profiles, Proceedings of ISSAC’13", ACM Press, New York (2013) 181-188. 8. Dumas J-G., Saunders B. D., Villard G., "On efficient sparse integer matrix Smith normal form computations", Jounal of Symbolic Computation, Vol. 32, Number 1/2 (2001) 71-99. 9. Hungerford T. W., "Algebra, Springer-Verlag", New York-Berlin (1980). 10. Kaplansky I., "Elementary divisors and modules", Trans. Amer. Math. Soc. 66, (1949) 464-491. 11. Kapur D., Cai Y., "An algorithm for computing a Gröbner basis of a polynomial ideal over a ring with zero divisors", Mathematics in Computer Science, Vol. 2, Number 4, (2009) 601-634. 12. Shores T., Wiegand R., "Decompositions of modules and matrices", Bull. Amer. Math. Soc. 79 (6) (1973) 1277-1280. 13. Wiegand R., Wiegand S., "Commutative rings whose finitely generated modules are direct sums of cyclics", Abelian group theory (Proc. Second New Mexico State Univ. Conf., Las Cruces, N.M., 1976), Lecture Notes in Math., Vol. 616, Springer, Berlin, (1977) 406-423.
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