| 16S32 | Rings of differential operators (associative algebraic aspects) |
| 47G20 | Integro-differential operators |
| 68W30 | Symbolic computation and algebraic computation |
| 32C38 | Sheaves of differential operators and their modules, \(D\)-modules |
| [1] | F. Baader and T. Nipkow. Term rewriting and all that. Cambridge University Press, Cambridge, 1998. |
| [2] | G. Baxter. An analytic problem whose solution follows from a simple algebraic identity. Pacific J. Math., 10:731-742, 1960. ·Zbl 0095.12705 |
| [3] | G. M. Bergman. The diamond lemma for ring theory. Adv. in Math., 29(2):178-218, 1978. ·Zbl 0326.16019 |
| [4] | R. Brüske, F. Ischebeck, and F. Vogel. Kommutative Algebra. Bibliographisches Institut, Mannheim, 1989. ·Zbl 0704.13001 |
| [5] | B. Buchberger. An algorithm for finding the bases elements of the residue class ring modulo a zero dimensional polynomial ideal (German). PhD thesis, Univ. of Innsbruck, 1965. ·Zbl 1245.13020 |
| [6] | B. Buchberger. Introduction to Gröbner bases. In{8}, pages 3-31. 1998. |
| [7] | B. Buchberger, G. Regensburger, M. Rosenkranz, and L. Tec. General polynomial reduction with Theorema functors: Applications to integro-differential operators and polynomials. ACM Commun. Comput. Algebra, 42(3):135-137, 2008. Poster presented at ISSAC’08. 10.1145/1504347.1504355 |
| [8] | B. Buchberger and F. Winkler, editors. Gröbner bases and applications, volume 251 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1998. |
| [9] | J. Bueso, J. Gómez-Torrecillas, and A. Verschoren. Algorithmic methods in non-commutative algebra. Kluwer Academic Publishers, Dordrecht, 2003. ·Zbl 1063.16054 |
| [10] | F. Chyzak and B. Salvy. Non-commutative elimination in Ore algebras proves multivariate identities. J. Symbolic Comput., 26(2):187-227, 1998. 10.1006/jsco.1998.0207 ·Zbl 0944.05006 |
| [11] | P. M. Cohn. Introduction to ring theory. Springer Undergraduate Mathematics Series. Springer-Verlag London Ltd., London, 2000. ·Zbl 1009.16001 |
| [12] | P. M. Cohn. Further algebra and applications. Springer-Verlag London Ltd., London, 2003. ·Zbl 1006.00001 |
| [13] | L. Gerritzen. Modules over the algebra of the noncommutative equation yx=1. Arch. Math. (Basel), 75(2):98-112, 2000. ·Zbl 0973.16017 |
| [14] | L. Guo. Baxter algebras and differential algebras. In Differential algebra and related topics (Newark, NJ, 2000), pages 281-305. World Sci. Publ., 2002. ·Zbl 1019.16013 |
| [15] | L. Guo and W. Keigher. On differential Rota-Baxter algebras. J. Pure Appl. Algebra, 212(3):522-540, 2008. ·Zbl 1185.16038 |
| [16] | N. Jacobson. Some remarks on one-sided inverses. Proc. Amer. Math. Soc., 1:352-355, 1950. ·Zbl 0037.15901 |
| [17] | E. Kolchin. Differential algebra and algebraic groups. Academic Press, New York-London, 1973. ·Zbl 0264.12102 |
| [18] | T. Y. Lam. A first course in noncommutative rings. Springer-Verlag, New York, 1991. ·Zbl 0728.16001 |
| [19] | V. Levandovskyy. Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation. PhD thesis, Universität Kaiserslauten, 2005. |
| [20] | J. C. McConnell and J. C. Robson. Noncommutative Noetherian rings. American Mathematical Society, Providence, RI, revised edition, 2001. ·Zbl 0980.16019 |
| [21] | T. Mora. An introduction to commutative and noncommutative Gröbner bases. Theoret. Comput. Sci., 134(1):131-173, 1994. 10.1016/0304-3975(94)90283-6 ·Zbl 0824.68056 |
| [22] | M. Z. Nashed and G. F. Votruba. A unified operator theory of generalized inverses. In M. Z. Nashed, editor, Generalized inverses and applications, pages 1-109. Academic Press, New York, 1976. ·Zbl 0356.47001 |
| [23] | K. B. Oldham and J. Spanier. The fractional calculus. Academic Press, New York-London, 1974. ·Zbl 0292.26011 |
| [24] | Ø. Ore. Theory of non-commutative polynomials. Ann. Math., 34:480-508, 1933. ·Zbl 0007.15101 |
| [25] | G. Regensburger and M. Rosenkranz. An algebraic foundation for factoring linear boundary problems. Ann. Mat. Pura Appl. (4), 188(1):123-151, 2009. ·Zbl 1181.47014 |
| [26] | M. Rosenkranz. A new symbolic method for solving linear two-point boundary value problems on the level of operators. J. Symbolic Comput., 39(2):171-199, 2005. 10.1016/j.jsc.2004.09.004 ·Zbl 1126.68104 |
| [27] | M. Rosenkranz and G. Regensburger. Integro-differential polynomials and operators. In D. Jeffrey, editor, Proceedings of ISSAC ’08, pages 261-268, New York, NY, USA, 2008. ACM. 10.1145/1390768.1390805 ·Zbl 1489.68415 |
| [28] | M. Rosenkranz and G. Regensburger. Solving and factoring boundary problems for linear ordinary differential equations in differential algebras. J. Symbolic Comput., 43(8):515-544, 2008. 10.1016/j.jsc.2007.11.007 ·Zbl 1151.34008 |
| [29] | G.-C. Rota. Baxter algebras and combinatorial identities. Bull. Amer. Math. Soc., 75:325-334, 1969. ·Zbl 0192.33801 |
| [30] | M. Saito, B. Sturmfels, and N. Takayama. Gröbner deformations of hypergeometric differential equations. Springer-Verlag, Berlin, 2000. ·Zbl 0946.13021 |
| [31] | V. Ufnarovski. Introduction to noncommutative Gröbner bases theory. In {8}, pages 259-280. 1998. ·Zbl 0902.16002 |
