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
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- [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
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- [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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