Remarks on Gröbner basis for ideals under composition
Wang Ming-sheng, Liu Zhuojun · 2001
Let K[x1,…,xn]be a polynomial ring over a field K in variables x1,…,xn, and K[y1,…,ym] be a polynomial ring over a field K in variables y1,…,ym. m n n. Let T = (t1,…,tn) be an ordered n-tuple of non-constant polynomials in K[y1,…,ym]. For any finite set F of K[x1,…,xn], let F o T be the set obtained from F by replacing xi; by ti, thus for any FeK[x1,…,xn], FoT eK[y1,…,ym]. With the above notations, Hong's main theorem [9] and the main theorem of [6] are generalized to general cases with some new proofs.