Central European Journal of Mathematics

, Volume 8, Issue 4, pp 780–785 | Cite as

Border bases and kernels of homomorphisms and of derivations

Research Article


Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations.


Border basis Gröbner basis Factorizable derivation Ideal of relations 


13N15 13P10 68W30 12Y05 12H05 


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Copyright information

© © Versita Warsaw and Springer-Verlag Wien 2010

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceNicholas Copernicus UniversityToruńPoland

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