Displaying similar documents to “The Algebraic Formulation: Why and How to Use it”

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 reflexivity of C(X,E) and Cambern's theorem

Fernanda Botelho, James Jamison (2008)

Studia Mathematica

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The algebraic and topological reflexivity of C(X) and C(X,E) are investigated by using representations for the into isometries due to Holsztyński and Cambern.

Two centuries of the term "algebraic analysis"

Danuta Przeworska-Rolewicz (2000)

Banach Center Publications

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The term "Algebraic Analysis" in the last two decades is used in two completely different senses. It seems that at least one is far away from its historical roots. Thus, in order to explain this misunderstanding, the history of this term from its origins is recalled.

Reduction of semialgebraic constructible functions

Ludwig Bröcker (2005)

Annales Polonici Mathematici

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Let R be a real closed field with a real valuation v. A ℤ-valued semialgebraic function on Rⁿ is called algebraic if it can be written as the sign of a symmetric bilinear form over R[X₁,. .., Xₙ]. We show that the reduction of such a function with respect to v is again algebraic on the residue field. This implies a corresponding result for limits of algebraic functions in definable families.

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...