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On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory
Differential Galois Theory Darboux theory of Integrability Poincar´ e problem,
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2011/2/24
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type folia-tion.
Polynomial identity rings as rings of functions, II
Polynomial identity ring central simple algebra trace ring
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2011/1/18
In characteristic zero, Zinovy Reichstein and the author generalized the usual relationship between irreducible Zariski closed subsets of the affine space.
Hopf algebras and polynomial identities
Polynomial identity Hopf algebra comodule localization
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2010/12/8
This is a survey of results obtained jointly with E. Aljadeff and published in [2]. We explain how to set up a theory of polynomial identities for comodule algebras over a Hopf algebra, and concentrat...
LINEAR COMPLEXITY AND THE MINIMAL POLYNOMIAL OF LINEAR RECURRING SEQUENCES OVER Z/(m)
Linear complexity over Z/(m) uniqueness
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2007/8/7
In this note we discuss the annihilating properties of sequences over Z/(m). By considering the linear complexity and the annihilator structure, we derive the uniqueness condition for the minimal poly...
Alternative Polynomial and Holomorphic Dunford-Pettis Properties
Alternative Polynomial Holomorphic Dunford-Pettis Properties
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2010/3/3
Alternatives to the Polynomial Dunford-Pettis property and the Holomorphic Dunford-Pettis property, called the PDP1 and HDP1 properties, respectively, are introduced. These are shown to be equivalent ...