Abstract:

Let A=K(θ)［a₁,…,a_n］ be a solvable polynomial algebra on a simple algebraic extension K(θ) of the field K, and the
subalgebra A₀=K［a₁,…,a_n］ of A be a solvable polynomial algebra on K. The structural relation between A and the polynomial algebra A₀［x］ shows the computation of left Grbner bases in A is effectively converted to the computation of left Grbner bases in A₀［x］.

Key words: solvable polynomial algebra, left ideal, left Grobner basis