An Application of Gro ̈bner Basis (International Journal of Scientific Research in Science and Technology, 2024)
We prove that the height of x_1 is 16 in A=Q[x_1,x_2,y_1,…,y_8 ]/I, where deg(x_i)=deg(y_i )=2i, and I is the ideal generated by the relation (1+x_1 +x_2 )(1 +y_1+⋯+y_8 )=1, using a Gro ̈bner basis technique. We discuss the topological implication and significance of computing the height of x_1.