Rational constants of monomial derivations

Nowicki, Andrzej; Zieliński, J.

doi:10.1016/j.jalgebra.2006.02.034

Cited by 17 publications

(19 citation statements)

References 13 publications

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“…Obviously, R = With the above notations we call δ the factorizable derivation associated with derivation . For more details we refer the reader to [7]. It is shown in [8] that if A (α) = 0, then the derivation δ has a nontrivial rational constant, and, an estimate can be given.…”

Section: Factorizable Derivations and Ideals Of Relationsmentioning

confidence: 99%

“…For instance, in [7], this tool gives a full and extensive description of all monomial derivations of [ ] with nontrivial rational constants, as well as other applications.…”

Section: Theorem 22 ([8] 65)mentioning

confidence: 99%

“…We show how to associate the factorizable derivation with any given derivation. The construction helps to establish new facts on our initial derivation, especially on its rational constants (see [7]). Furthermore we define an ideal of relations associated with a derivation and we estimate the number of generators of the ideal of relations.…”

Section: Introductionmentioning

confidence: 99%

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Border bases and kernels of homomorphisms and of derivations

Zieliński

2010

Open Mathematics

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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. MSC:13N15, 13P10, 68W30, 12Y05, 12H05

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Section: Factorizable Derivations and Ideals Of Relationsmentioning

confidence: 99%

“…For instance, in [7], this tool gives a full and extensive description of all monomial derivations of [ ] with nontrivial rational constants, as well as other applications.…”

Section: Theorem 22 ([8] 65)mentioning

confidence: 99%

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Border bases and kernels of homomorphisms and of derivations

Zieliński

2010

Open Mathematics

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“…The way how to associate the factorizable derivation with a given derivation is presented in [10]. The construction helps to establish new facts on constants of the initial derivation (see, for instance, [8]). We thus have a special interest in describing constants of factorizable derivations.…”

Section: Introductionmentioning

confidence: 99%

Rings of constants of four-variable Lotka-Volterra systems

Zieliński

2013

Open Mathematics

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Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameterswhere is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations. MSC:13N15, 12H05, 92D25, 34A34

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“…How to associate a factorizable derivation with any given derivation is shown in [10]. The construction helps to establish new facts on constants of the initial derivation (see, for instance, [8]). We have thus a special interest in describing constants of factorizable derivations.…”

Section: Introductionmentioning

confidence: 99%