An Algebraic Treatment of Totally Linear Partial Differential Equations

dc.creatorViazminsky, C. P.
dc.date1999-07-14
dc.date.accessioned2026-07-07T05:29:54Z
dc.date.available2026-07-07T05:29:54Z
dc.descriptionWe construct the field A generated by n algebraically independent elements, and show that the linear space of derivations over this field is faithfully represented by the linear space of the n-th fold Cartesian product of this field acting through inner product on the gradient of this field. We prove also that functional independence of a set in this field is equivalent to linear independence of the gradient set in the space of Cartesian product. It is shown that every subfield S of A which is generated by (n-1) functionally independent elements defines an one-dimensional space of derivations, such that each member L of the latter subspace has S as its kernel. Each coset of the multiplicative subgroup S defines a non-homogeneous differential operator L+q whose kernel coincide with this coset. We prove also that every element of A defines a coset of the subgroup ker(L+q) in the additive group A, on which L+q is constant.
dc.identifierhttps://arxiv.org/abs/math/9907091
dc.identifierhttp://arxiv.org/abs/math/9907091
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78824
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subjectRings and Algebras
dc.titleAn Algebraic Treatment of Totally Linear Partial Differential Equations
dc.typetext

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