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math.RA2008★ 12 cited
Composition-Diamond lemma for differential algebras
Yuqun Chen, Yongshan Chen, Yu Li
In this paper, we establish the Composition-Diamond lemma for free differential algebras. As applications, we give Groebner-Shirshov bases for free Lie-differential algebra and fre…
math.RA2008★ 13 cited
Anti-commutative Groebner-Shirshov basis of a free Lie algebra
L. A. Bokut, Yuqun Chen, Yu Li
One of the natural ways to prove that the Hall words (Philip Hall, 1933) consist of a basis of a free Lie algebra is a direct construction: to start with a linear space spanned by…
math.RA2008
Some remarks for the Akivis algebras and the Pre-Lie algebras
Yuqun Chen, Yu Li
In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and…