On the D-bases of polynomial ideals over principal ideal domains

DOI10.1016/S0747-7171(89)80006-9zbMath0668.68034MaRDI QIDQ1118398

Luquan Pan

Publication date: 1989

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

zbMATH Keywords

Gröbner basesprincipal ideal domainspolynomial idealcritical-pair/completionD-basesD-reductionseuclidean domain

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Principal ideal rings (13F10) Polynomials over commutative rings (13B25) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Euclidean rings and generalizations (13F07)

Related Items (12)

Signature Gröbner bases in free algebras over rings ⋮ De Nugis Groebnerialium 7: Janet, Gerdt, Tamari ⋮ Standard bases over Euclidean domains ⋮ Semi-ring Based Gröbner–Shirshov Bases over a Noetherian Valuation Ring ⋮ Gröbner bases with coefficients in rings ⋮ A general framework for Noetherian well ordered polynomial reductions ⋮ Standard Gröbner-Shirshov Bases of Free Algebras Over Rings, I ⋮ On lucky ideals for Gröbner basis computations ⋮ Buchberger-Zacharias theory of multivariate Ore extensions ⋮ Toward involutive bases over effective rings ⋮ Zacharias representation of effective associative rings ⋮ On Gröbner bases under specialization

Cites Work

• Computing a Gröbner basis of a polynomial ideal over a Euclidean domain
• Über B. Buchbergers Verfahren, Systeme algebraischer Gleichungen zu lösen
• Comments on the translation of my PhD thesis: ``An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
• The Euclidean algorithm
• A Canonical Basis for the Ideals of a Polynomial Domain
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