On Finite Noncommutative Gr(o)bner Bases

• 作者: Yatma Diop Djiby Sow
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 381-388
• 页数: 8页
• 语种: 英文
• DOI: 10.1142/S1005386720000310

摘要

It is well known that in the noncommutative polynomial ring in serveral variables Buchberger's algorithm does not always terminate.Thus,it is important to characterize noncommutative ideals that admit a finite Gr(o)bner basis.In this context,Eisenbud,Peeva and Sturmfels defined a map γ from the noncommutative polynomial ring k<X1,…,Xn> to the commutative one k[x1,…,xn]and proved that any ideal J of k<X1,…,Xn>,written as J =γ-1(I) for some ideal I of k[x1,…,xn],amits a finite Gr(o)bner basis with respect to a special monomial ordering on k<X1,…,Xn).In this work,we approach the opposite problem.We prove that under some conditions,any ideal J of k<X1,…,Xn> admitting a finite Gr(o)bner basis can be written as J =γ-1(I) for some ideal I of k[x1,…,xn].