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Displaying similar documents to “Polynomial Riccati equations with algebraic solutions”

Note on algebraic interior systems

Ivan Chajda (2005)

Discussiones Mathematicae - General Algebra and Applications

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We get an interrelation between an algebraic closure system and its conjugated interior system. We introduce the concept of algebraic interior system and we get its representation.

Algebraic Numbers

Yasushige Watase (2016)

Formalized Mathematics

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This article provides definitions and examples upon an integral element of unital commutative rings. An algebraic number is also treated as consequence of a concept of “integral”. Definitions for an integral closure, an algebraic integer and a transcendental numbers [14], [1], [10] and [7] are included as well. As an application of an algebraic number, this article includes a formal proof of a ring extension of rational number field ℚ induced by substitution of an algebraic number to...

Multiplicative dependence of shifted algebraic numbers

Paulius Drungilas, Artūras Dubickas (2003)

Colloquium Mathematicae

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We show that the set obtained by adding all sufficiently large integers to a fixed quadratic algebraic number is multiplicatively dependent. So also is the set obtained by adding rational numbers to a fixed cubic algebraic number. Similar questions for algebraic numbers of higher degrees are also raised. These are related to the Prouhet-Tarry-Escott type problems and can be applied to the zero-distribution and universality of some zeta-functions.