| ### 7.4.4 References (plural) The Centre for Computer Algebra Kaiserslautern publishes a series of preprints which are electronically available at https://www.mathematik.uni-kl.de/organisation/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 http://krum.rz.uni-mannheim.de/kredel/kredel_solvable_polynomial_rings.pdf [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 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. A. Kandri-Rody and V. Weispfenning. Non-commutative Gröbner bases in algebras of solvable type. J. Symbolic Computation, 9(1):1-26, 1990. [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. https://www.mathematik.uni-kl.de/organisation/zca/reports-on-ca/. 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.

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