Central European Journal of Mathematics

, Volume 8, Issue 4, pp 780–785

# Border bases and kernels of homomorphisms and of derivations

Research Article

## Abstract

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.

### Keywords

Border basis Gröbner basis Factorizable derivation Ideal of relations

### MSC

13N15 13P10 68W30 12Y05 12H05

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