On the finite dual of a cocommutative Hopf algebroid. Application to linear differential matrix equations and Picard-Vessiot theory.

The Picard-Vessiot Theory of Homogeneous Linear Ordinary Differential Equations.

A Categorical Approach to Picard-vessiot Theory

Picard-Vessiot rings are present in many settings like differential Galois theory, difference Galois theory and Galois theory of Artinian simple module algebras. In this article we set up an abstract framework in which we can prove theorems on existence and uniqueness of Picard-Vessiot rings, as well as on Galois groups corresponding to the Picard-Vessiot rings. As the present approach restrict...

Relative invariants, difference equations, and the Picard-Vessiot theory

Acknowledgements First of all I would like to thank my supervisor Professor T. Kimura. He taught me how to learn mathematics from the beginning when I just started afresh my life. About four years ago he suggested to study on archimedean local zeta functions of several variables as my first research task for the Master's thesis. I can not give enough thanks to his heartwarming encouragement all...

Generic Rings for Picard–Vessiot Extensions and Generic Differential Equations

Let G be an observable subgroup of GLn. We produce an extension of differential commutative rings generic for Picard–Vessiot extensions with

on the effect of linear & non-linear texts on students comprehension and recalling

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