ON CANONICAL BASES OF VECTOR SPACES WITH A WELL-ORDERED BASIS AND A DISTINGUISHED FAMILY OF SUBSPACES

摘要

Let V be a vector space with a well-ordered basis and 3 be a family of subspaces of V closed under intersections. An analog of the Groebner basis is defined for subspaces from 3. It is shown that in the Noetherian case, such a basis always exists and is unique.