可除的四元数代数上多项式环的Grobner基

设F是一个特征不等于2的域，A是，上的一个可除代数。本文研究了A上多项式环Ax1，X2，…，xn]中理想是有限生成的，以及它的Grobner基；也表明Fx1，x2，…，xn]中有限子集G是Fx1，x2，…，xn]的Griobner基当且仅当G是Ax1，x2，…，xn]中的Grobner基。

Grobner Bases in Polynomial Rings over a Division Quaternion Algebra

Let F be a field whose characteristic is not 2 and A be a division quaternion algebra over a field F. In this paper, first we will investigate the structure of the ideals in polynomial rings A x1 ,x2 ,……,xn ] over a division quaternion algebra A. It is shown that the ideal I in Ax1 ,x2 ,...,x,,] is finitely generated. Secondly we will consider Grisbner bases for ideals in polynomial ring A x1 ,x2 ,……,xn ] . We show that a finite subset G of F x l, x2 ,＇＂,xn ] is a Griibner basis in Fx1 ,x2 ,…… ,xn] if and only if G is a Grobner basis inAx1 ,x2 ,…… ,xn].