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7.4.4 References (plural)

The Centre for Computer Algebra Kaiserslautern publishes a series of preprints which are electronically available at http://www.mathematik.uni-kl.de/~zca/Reports_on_ca. Other sources to check are the following books and articles:

Text books

  • [DK] Y. Drozd and V. Kirichenko. Finite dimensional algebras. With an appendix by Vlastimil Dlab. Springer, 1994

  • [GPS] Greuel, G.-M. and Pfister, G. with contributions by Bachmann, O. ; Lossen, C. and Schönemann, H. A SINGULAR Introduction to Commutative Algebra. Springer, 2002

  • [BGV] Bueso, J.; Gomez Torrecillas, J.; Verschoren, A. Algorithmic methods in non-commutative algebra. Applications to quantum groups. Kluwer Academic Publishers, 2003

  • [Kr] Kredel, H. Solvable polynomial rings. Shaker, 1993

  • [Li] Huishi Li. Non-commutative Gröbner bases and filtered-graded transfer. Springer, 2002

  • [MR] McConnell, J.C. and Robson, J.C. Non-commutative Noetherian rings. With the cooperation of L. W. Small. Graduate Studies in Mathematics. 30. Providence, RI: American Mathematical Society (AMS)., 2001

Descriptions of algorithms and problems

  • Havlicek, M. and Klimyk, A. and Posta, S. Central elements of the algebras $U'_q({\rm so}_m)$ and $U'_q({\rm iso}_m)$. arXiv. math. QA/9911130, (1999)

  • J. Apel. Gröbnerbasen in nichtkommutativen algebren und ihre anwendung. Dissertation, Universität Leipzig, 1988.

  • Apel, J. Computational ideal theory in finitely generated extension rings. Theor. Comput. Sci.(2000), 244(1-2):1-33

  • O. Bachmann and H. Schönemann. Monomial operations for computations of Gröbner bases. In Reports On Computer Algebra 18. Centre for Computer Algebra, University of Kaiserslautern (1998)

  • D. Decker and D. Eisenbud. Sheaf algorithms using the exterior algebra. In Eisenbud, D.; Grayson, D.; Stillman, M.; Sturmfels, B., editor, Computations in algebraic geometry with Macaulay 2, (2001)

  • Jose L. Bueso, J. Gomez Torrecillas and F. J. Lobillo. Computing the Gelfand-Kirillov dimension II. In A. Granja, J. A. Hermida and A. Verschoren eds. Ring Theory and Algebraic Geometry, Lect. Not. in Pure and Appl. Maths., Marcel Dekker, 2001.

  • Jose L. Bueso, J. Gomez Torrecillas and F. J. Lobillo. Re-filtering and exactness of the Gelfand-Kirillov dimension. Bulletin des Sciences Mathematiques 125(8), 689-715 (2001).

  • J. Gomez Torrecillas and F.J. Lobillo. Global homological dimension of multifiltered rings and quantized enveloping algebras. J. Algebra, 225(2):522-533, 2000.

  • N. Iorgov. On the Center of $q$-Deformed Algebra $U'_q( \rm so _3)$ Related to Quantum Gravity at $q$ a Root of $1$.In Proceedings of IV Int. Conf. "Symmetry in Nonlinear Mathematical Physics",(2001) Kyiv, Ukraine

  • A. Kandri-Rody and V. Weispfenning. Non-commutative Gröbner bases in algebras of solvable type. J. Symbolic Computation, 9(1):1-26, 1990.

  • Levandovskyy, V. On Gröbner bases for non-commutative G-algebras. In Kredel, H. and Seiler, W.K., editor, Proceedings of the 8th Rhine Workshop on Computer Algebra, 2002.

  • [L1] Levandovskyy, V. PBW Bases, Non-degeneracy Conditions and Applications. In Buchweitz, R.-O. and Lenzing, H., editor, Proceedings of the ICRA X conference, Toronto, 2003.

  • [LS] Levandovskyy V.; Schönemann, H. Plural - a computer algebra system for non-commutative polynomial algebras. In Proc. of the International Symposium on Symbolic and Algebraic Computation (ISSAC'03). ACM Press, 2003.

  • [LV] Levandovskyy, V. Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation. Doctoral Thesis, Universität Kaiserslautern, 2005. Available online at http://kluedo.ub.uni-kl.de/volltexte/2005/1883/.

  • [L2] Levandovskyy, V. On preimages of ideals in certain non-commutative algebras. In Pfister G., Cojocaru S. and Ufnarovski, V. (editors), Computational Commutative and Non-Commutative Algebraic Geometry, IOS Press, 2005.

  • Mora, T. Gröbner bases for non-commutative polynomial rings. Proc. AAECC 3 Lect. N. Comp. Sci, 229: 353-362, 1986.

  • Mora, T. An introduction to commutative and non-commutative Groebner bases. Theor. Comp. Sci., 134: 131-173, 1994.

  • T. Nüßler and H. Schönemann. Gröbner bases in algebras with zero-divisors. Preprint 244, Universität Kaiserslautern, 1993. Available online at http://www.mathematik.uni-kl.de/~zca/Reports_on_ca/index.html.

  • Schönemann, H. SINGULAR in a Framework for Polynomial Computations. In Joswig, M. and Takayama, N., editor, Algebra, Geometry and Software Systems, pages 163-176. Springer, 2003.

  • T. Yan. The geobucket data structure for polynomials. J. Symbolic Computation, 25(3):285-294, March 1998.