摘要
The filtered-graded transfer of SAGBI bases computation in solvable polynomial algebras was considered. The relations among the SAGBI bases of a subalgebra B, its associated graded algebra G(B) and Rees algebra B were got. These relations solve a natural question: how to determine the generating set of G(B) and B from any given generating set of B. Based on these some equivalent conditions for the existence of finite SAGBI bases can be got.
The filtered-graded transfer of SAGBI bases computation in solvable polynomial algebras was considered. The relations among the SAGBI bases of a subalgebra B, its associated graded algebra G(B) and Rees algebra B were got. These relations solve a natural question: how to determine the generating set of G(B) and B from any given generating set of B. Based on these some equivalent conditions for the existence of finite SAGBI bases can be got.
