Narrow Results

Using Buchberger–Shirshov Algorithm, Composition–Diamond Lemma and partitions of integers we obtain the reduced Gröbner–Shirshov basis of Ã_n and classify all reduced words of the affine Weyl group Ã_n.

In this paper, we establish Composition-Diamond lemma for multiple tensor products of commutative algebra $k[Y]$, free associative algebras $k〈X^{(i)}〉$, Grassman algebras $G_k(Z^{(j)})$ and path algebras ${\mathrm{\text{path}}}_k(\overrightarrow{P^{(l)}})$ over a field $k$.

In this survey article, we report some new results of Gröbner-Shirshov bases, including new Composition-Diamond lemmas, applications of some known Composition-Diamond lemmas and content of some expository papers.

In this paper, Gröbner—Shirshov bases and normal forms of elements for the Coxeter groups E₆ and E₇ are found. These results support the conjecture in [4] about the general form of Gröbner—Shirshov bases for all Coxeter groups.

In this survey article, we report some new results of Gröbner-Shirshov bases, including new Composition-Diamond lemmas and some applications of some known Composition-Diamond lemmas.