Journal of Mathematical Sciences

, Volume 192, Issue 2, pp 247–249 | Cite as

On Canonical Bases of Vector Spaces with a Well-Ordered Basis and a Distinguished Family of Subspaces


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


Vector Space Canonical Base Distinguish Family Groebner Basis Noetherian Case 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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