- 1.BERSTEL, J., AND PERRIN, D. Theory of codes, vol. 117 of Pure and Applied Mathematics. Academic Press Inc., Orlando, Fla., 1985. Google ScholarDigital Library
- 2.BUCHBERGER, B. On finding a vector space basis of the residue class ring modulo a zero dimensional polynomial ideal (German). PhD thesis, University of Innsbruck, Austria, 1965.Google Scholar
- 3.KAPUR, D., AND MADLENER, K. A completion procedure for computing a canonical basis for a ksubalgebra. In Computers and mathematics (Cambridge, MA, 1989). Springer, New York, 1989, pp. 1-11. Google ScholarCross Ref
- 4.MORA, F. Groebner bases for noncommutative polynomial rings. In Algebraic algorithms and error correcting codes (Grenoble, 1985), vol. 229 of Lecture Notes in Comput. Sci. Springer, Berlin, 1986, pp. 353-362. Google Scholar
- 5.NORDBECK, P. On some basic applications of GrSbner bases in noncommutative polynomial rings. In GrSbner bases and applications, vol. 251 of London Math. Soc. Lecture Note Ser. Cambridge Univ. Press, Cambridge, 1993, pp. 463-472.Google Scholar
- 6.OLLIVIER, F. Canonical bases: relations with standard bases, finiteness conditions and application to tame automorphisms. In Effective methods in algebraic geometry (Castiglioncello, 1990), vol. 94 of Progr. Math. Birkh/iuser Boston, Boston, MA, 1991, pp. 379-400.Google Scholar
- 7.PODOPLELOV, A., AND UFNAROVSKI, V. ANICK, C code, 1997. Available by anonymous ftp from ftp.riscom.net in the directory: /pub/anick.Google Scholar
- 8.ROBBIANO, L., AND SWEEDLER, M. Subalgebra bases. In Commutative algebra (Salvador, 1988), vol. 1430 of Lecture Notes in Math. Springer, Berlin, 1990, pp. 61- 87.Google Scholar
- 9.SHANNON, D., AND SWEEDLER, M. Using GrSbner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence. J. Symbolic Comput. 6, 2-3 (1988), 267-273. Computational aspects of commutative algebra. Google ScholarDigital Library
- 10.STURMFELS, B. GrSbner bases and convex polytopes, vol. 8 of University Lecture Series. American Mathematical Society, Providence, RI, 1996.Google Scholar
- 11.UFNAROVSKI, V. Combinatorial and asymptotic methods in algebra {MR 92h:16024}. In Algebra, VI, vol. 57 of Encyclopaedia Math. Sci. Springer, Berlin, 1995, pp. 1- 196.Google Scholar
Index Terms
- Canonical subalgebraic bases in non-commutative polynomial rings
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