Composition-Diamond lemma for tensor product of free algebras

被引：16

作者：

Bokut, L. A. ^{[1
,2
]}

Chen, Yuqun ^{[1
]}

Chen, Yongshan ^{[1
]}

机构：

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] Russian Acad Sci, Sobolev Inst Math, Siberian Branch, Novosibirsk 630090, Russia

来源：

JOURNAL OF ALGEBRA | 2010年 / 323卷 / 09期

关键词：

Grobner-Shirshov basis; Grobner basis; Free algebra; Polynomial algebra; Tensor product; GROBNER BASES; SINGULARITIES; RESOLUTION; VARIETY; FIELD;

D O I：

10.1016/j.jalgebra.2010.02.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish a Composition-Diamond lemma for the tensor product k < X > circle times k < Y > of two free algebras over a field. As an application, we construct a Grobner-Shirshov basis in k < X > circle times k < Y > by lifting a given Grobner-Shirshov basis in the tensor product kinverted right perpendicularXinverted left perpendicular circle times k < Y > in which kinverted right perpendicularXinverted left perpendicular is the polynomial algebra. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2520 / 2537

页数：18

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