- B. Buchberger. An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Polynomial Ideal (in German). Ph.D. thesis, University of Innsbruck, Austria. (reprinted in Buchberger (2006)).Google Scholar
- B. Buchberger. Bruno Buchberger's phd thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Journal of Symbolic Computation 41, 475--51, 2006. Google ScholarDigital Library
- A. Dukkipati, N. Pai, M. Francis & A. Dubey. Macaulay-Buchberger basis theorem for residue class rings with torsion and border bases over rings Preprint, available at http://arxiv.org/abs/1405.0472, 2014.Google Scholar
- A. Dukkipati & M. Francis. On reduced Gröbner bases and Macaulay-Buchberger basis theorem over noetherian rings. Journal of Symbolic Computation 65, 1--14, 2014.Google ScholarCross Ref
- F. S. Macaulay. The Algebraic Theory of Modular Systems. The Cornell Library of Historical Mathematical Monographs. Cambridge University Press, 1916.Google Scholar
Index Terms
- On Gröbner bases over rings and residue class polynomial rings with torsion
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