Some criteria for Groebner bases and their applications

摘要

We consider the following two problems: Let f and g be two polynomials over a field K.P1. When is {f + s, g + t} a Grobner basis for all s, t is an element of K?P2. When is {f(lambda), g(sigma)} a Grobner basis for all lambda, sigma is an element of N?We provide a simpler proof of Hoon's criterion for P1 and a new criterion for P2. The two criteria are applied to the theory of Grobner bases under composition. (C) 2017 Elsevier Ltd. All rights reserved.