# Border bases and kernels of homomorphisms and of derivations

Open Mathematics (2010)

- Volume: 8, Issue: 4, page 780-785
- ISSN: 2391-5455

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topJanusz Zieliński. "Border bases and kernels of homomorphisms and of derivations." Open Mathematics 8.4 (2010): 780-785. <http://eudml.org/doc/268991>.

@article{JanuszZieliński2010,

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.},

author = {Janusz Zieliński},

journal = {Open Mathematics},

keywords = {Border basis; Gröbner basis; Factorizable derivation; Ideal of relations; border basis; factorizable derivation; ideal of relations},

language = {eng},

number = {4},

pages = {780-785},

title = {Border bases and kernels of homomorphisms and of derivations},

url = {http://eudml.org/doc/268991},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Janusz Zieliński

TI - Border bases and kernels of homomorphisms and of derivations

JO - Open Mathematics

PY - 2010

VL - 8

IS - 4

SP - 780

EP - 785

AB - 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.

LA - eng

KW - Border basis; Gröbner basis; Factorizable derivation; Ideal of relations; border basis; factorizable derivation; ideal of relations

UR - http://eudml.org/doc/268991

ER -

## References

top- [1] Chen Y.F., Meng X.H., Border bases of positive dimensional polynomial ideals, In: Proceedings of the 2007 International Workshop on Symbolic-Numeric Computation, London, Ontario, July 25–27, ACM, New York, 2007, 65–71
- [2] Gianni P., Trager B., Zacharias G., Gröbner bases and primary decomposition of polynomial ideals, J. Symbolic Comput., 1988, 6(2–3), 149–167 http://dx.doi.org/10.1016/S0747-7171(88)80040-3[Crossref] Zbl0667.13008
- [3] Kehrein A., Kreuzer M., Characterizations of border bases, J. Pure Appl. Algebra, 2005, 196(2–3), 251–270 http://dx.doi.org/10.1016/j.jpaa.2004.08.028[Crossref] Zbl1081.13011
- [4] Kehrein A., Kreuzer M., Computing border bases, J. Pure Appl. Algebra, 2006, 205(2), 279–295 http://dx.doi.org/10.1016/j.jpaa.2005.07.006[Crossref]
- [5] Kehrein A., Kreuzer M., Robbiano L., An algebraist’s view on border bases, In: Solving polynomial equations, Algorithms Comput. Math., 14, Springer, Berlin, 2005, 169–202 http://dx.doi.org/10.1007/3-540-27357-3_4[Crossref] Zbl1152.13304
- [6] Kreuzer M., Robbiano L., Computational Commutative Algebra, 1&2, Springer, Berlin, 2000&2005 http://dx.doi.org/10.1007/978-3-540-70628-1[Crossref]
- [7] Nowicki A., Zielinski J., Rational constants of monomial derivations, J. Algebra, 2006, 302(1), 387–418 http://dx.doi.org/10.1016/j.jalgebra.2006.02.034[Crossref] Zbl1119.13021
- [8] Zieliński J., Factorizable derivations and ideals of relations, Comm. Algebra, 2007, 35(3), 983–997 http://dx.doi.org/10.1080/00927870601117639[WoS][Crossref] Zbl1171.13013

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