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Let K be a field and R = ⊕ p∈N R p an N-graded K-algebra, which has an SM K-basis (i.e. a skew multiplicative K-basis) such that R holds a Gröbner basis theory. It is proved that there is a one-to-one correspondence between the set of Gröbner bases in R and the set of dh-closed homogeneous Gröbner bases in the polynomial algebra R[t]; and that the similar(More)
In this paper, we introduce (almost) skew 2-nomial algebras, establish the existence of a skew multiplicative K-basis for a skew 2-nomial algebra, and explore the existence of a Gröbner basis theory for such algebras. Let K be a field, and let R be a finitely generated free K-algebra, or a path algebra defined by a finite directed graph over K. Then it is(More)
By employing the (de)homogenization technique in a relatively extensive setting, this note studies in detail the relation between non-homogeneous Gröbner bases and homogeneous Gröbner bases. As a consequence , a general principle of computing Gröbner bases (for an ideal and its homogenization ideal) by passing to homogenized generators is clarified(More)
  • Huishi Li
  • 2014
In terms of their defining relations, solvable polynomial algebras introduced by Kandri-Rody and Weispfenning [J. Symbolic Comput., 9(1990)] are characterized by employing Gröbner bases of ideals in free algebras, thereby solvable polynomial algebras are completely determinable and constructible in a computational way.
Let R be an arbitrary commutative ring and RX = RX 1 ,. the free algebra of n generators over R. Note that Bergman's diamond lemma characterizes the resolvability of ambiguities of monic relations of the form W σ − f σ with f σ a linear combination of monomials ≺ W σ , where ≺ is a semigroup partial ordering on X; and that in the algorithmic language of(More)
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