Corpus ID: 199528261

A localized version of the basic triangle theorem

@article{Duchamp2019ALV,
  title={A localized version of the basic triangle theorem},
  author={G. Duchamp and N. Gargava},
  journal={ArXiv},
  year={2019},
  volume={abs/1908.03327}
}
In this short note, we give a localized version of the basic triangle theorem, first published in 2011 (see [4]) in order to prove the independence of hyperlogarithms over various function fields. This version provides direct access to rings of scalars and avoids the recourse to fraction fields as that of meromorphic functions for instance. 

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References

SHOWING 1-10 OF 11 REFERENCES
Independence of Hyperlogarithms over Function Fields via Algebraic Combinatorics
TLDR
This work obtains a necessary and sufficient condition for the linear independence of solutions of differential equations for hyperlogarithms and extends the property of linear independence to the largest known ring of coefficients. Expand
Free partially commutative structures
Abstract In this paper, we study algebraic structures defined by a presentation of the form 〈 A; ab = ba for (a, b) ∈ I 〉. We show that these relators are the only one that can be interpreted as bothExpand
Kleene stars of the plane, polylogarithms and symmetries
TLDR
Algebraic and analytic aspects of this extension allowing index polylogarithms at non positive multi-indices, by rational series and regularize polyzetas at non negative multi-Indices are concentrated on. Expand
On the exponential solution of differential equations for a linear operator
The present investigation was stimulated by a recent paper of K. 0. Friedrichs 113, who arrived at some purely algebraic problems in connection with the theory of linear operators in quantumExpand
Free Differential Calculus, IV. The Quotient Groups of the Lower Central Series
The quotient groups Qn(G) =GnGn+i of the lower central series G = G1 D G, D G, D * * of a finitely generated group G are finitely generated abelian groups. Our object is to develop an algorithm forExpand
Rational series and their languages
TLDR
This chapter discusses the development of Rational Series over a Principal Ring, a model based on the model developed in Chapter I, and its applications to Languages and Codes. Expand
Solomon.– Independence of hyperlogarithms over function fields via algebraic combinatorics, in Lecture Notes in Computer Science
  • 2011
Theory of Sets, Springer-Verlag Berlin and Heidelberg GmbH & Co. K; (2nd printing
  • 2004
Commutative Algebra: Chapters
  • 1998
If the image (through a A-linear arrow) of a family is A-free then the family itself is A-free
    ...
    1
    2
    ...