References

Journal of Mathematical Sciences: Advances and Applications

TESTING FREENESS OVER HERMITE RINGS

[1] F. Chyzak, A. Quadrat and D. Robertz, Effective algorithms for parametrizing linear control systems over Ore algebras, AAECC 16 (2005), 319-376.

[2] T. Cluzeau and A. Quadrat, Factoring and decomposing a class of linear functional systems, Lin. Alg. and its Appl. 428 (2008), 324-381.

[3] A. Fabiańska and A. Quadrat, Applications of the Quillen-Suslin theorem to multirankal systems theory, INRIA, Rapport de Recherche 6126 (2007).

[4] J. Gago-Vargas, On Suslin’s Stability Theorem for Ring Theory and Algebraic Geometry, Lecture Notes in Pure and Applied Mathematics, Vol. 221, Marcel Dekker, New York, (2001), 203-210.

[5] G. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, 2nd edition, Springer, 2007.

[6] T. Y. Lam, Serre’s Problem on Projective Modules, Springer Monographs in Mathematics, Springer, 2006.

[7] S. Lang, Algebra, Springer, 2004.

[8] R. C. Laubenbacher and C. Woodburn, An algorithm for the Quillen-Suslin theorem for monoid rings, J. Pure Appl. Algebra 117-118 (1997), 395-429.

[9] R. C. Laubenbacher and K. Schlauch, An algorithm for the Quillen-Suslin theorem for quotients of polynomial rings by monomial ideals, J. Symb. Comp. 30 (2000), 555-571.

[10] R. C. Laubenbacher and C. Woodburn, A new algorithm for the Quillen-Suslin theorem, Contributions to Algebra and Geometry 41 (2000), 23-31.

[11] O. Lezama, Gröbner bases for modules over Noetherian polynomial commutative rings, Georgian Mathematical Journal 15 (2008), 121-137.

[12] O. Lezama, Some applications of Gröbner bases in homological algebra, São Paulo Journal of Mathematical Sciences 3(1) (2009), 25-59.

[13] O. Lezama et al., Quillen-Suslin rings, Extracta Mathematicae 24(1) (2009).

[14] A. Logar and B. Sturmfels, Algorithms for the Quillen-Suslin theorem, J. Algebra 145(1) (1992).

[15] H. Lombardi, Le contenu constructif d’un principe local-global avec une application á la structure d’un module projectif de type fini, Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 1997.

[16] H. Lombardi and Quitté, Algèbre Commutative, Méthodes Constructives, Modules Projectifs de Type Fini, 2009:
hlombardi.free.fr/

[17] B. MacDonald, Linear Algebra over Commutative Rings, Marcel Dekker, 1984.

[18] H. Park and C. Woodburn, An algorithmic proof of Suslin’s stability theorem for polynomial rings, J. Algebra 178 (1995), 277-298.

[19] A. Quadrat and D. Robertz, Computation of bases of free modules over the Weyl algebras, Journal of Symbolic Computation (2007), doi:10.1016/j.jsc.2007.06.005.

[20] D. Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167-171.

[21] J. J. Rotman, An Introduction to Homological Algebra, Academic Press, 1979.

[22] A. A. Suslin, Projective modules over polynomial rings are free, Soviet Math. Dokl. 17 (1976), 1160-1164.