Noncommutative Grobner Bases for Almost Commutative Algebras
| dc.creator | Li, Huishi | |
| dc.date | 2007-01-04 | |
| dc.date.accessioned | 2026-07-07T07:38:35Z | |
| dc.date.available | 2026-07-07T07:38:35Z | |
| dc.description | Let $K$ be an infinite field and $K< X> =K< X_1,...,X_n>$ the free associative algebra generated by $X=\{X_1,...,X_n\}$ over $K$. It is proved that if $I$ is a two-sided ideal of $K< X>$ such that the $K$-algebra $A=K< X> /I$ is almost commutative in the sense of [3], namely, with respect to its standard $\mathbb{N}$-filtration $FA$, the associated $\mathbb{N}$-graded algebra $G(A)$ is commutative, then $I$ is generated by a finite Gröbner basis. Therefor, every quotient algebra of the enveloping algebra $U(\mathbf{g})$ of a finite dimensional $K$-Lie algebra $\mathbf{g}$ is, as a noncommutative algebra of the form $A=K< X> /I$, defined by a finite Gröbner basis in $K< X>$. | |
| dc.description | 7pages | |
| dc.identifier | https://arxiv.org/abs/math/0701120 | |
| dc.identifier | http://arxiv.org/abs/math/0701120 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121139 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16W70; 16Z05 | |
| dc.title | Noncommutative Grobner Bases for Almost Commutative Algebras | |
| dc.type | text |