On Finite Noncommutative Grobner Bases  

作　　者：Yatma Diop Djiby Sow 

机构地区：[1]Department of Mathematics and Computer Sciences Cheikh Anta Diop University of Dakar,Dakar,Senegal

出　　处：《Algebra Colloquium》2020年第3期381-388,共8页代数集刊（英文版）

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 Grobner basis.In this context,Eisenbud,Peeva and Sturmfels defined a mapγfrom the noncommutative polynomial ring k〈X_(1),...,X_(n)〉to the commutative one k[x_(1),...,x_(n)]and proved that any ideal J of k〈X_(1),...,X_(n)〉,written as J=γ^(-1)(L)for some ideal L of k[x_(1),...,x_(n)],amits a finite Grobner basis with respect to a special monomial ordering on k〈X_(1),...,X_(n)〉.In this work,we approach the opposite problem.We prove that under some conditions,any ideal J of k〈X_(1),...,X_(n)〉admitting a finite Grobner basis can be written as J=γ^(-1)(L)for some ideal L of k[x_(1),...,x_(n)].

关 键 词：natural maps lexicographic extension minimal generators COMMUTATORS 

分 类 号：O15[理学—数学]