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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Analytic real algebras.

Young Joo Seo1, Young Hee Kim2

  • 1Department of Mathematics, Research Institute for Natural Sci., Hanyang University, Seoul, 04763 Korea.

Springerplus
|October 19, 2016
PubMed
Summary
This summary is machine-generated.

This study constructs real algebras using elementary functions. It identifies conditions for real-valued functions to qualify as d-algebras, advancing algebraic function theory.

Keywords:
Analytic real algebraBCK-algebraTraced-algebra

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Area of Science:

  • Algebra
  • Real Analysis
  • Function Theory

Background:

  • Real algebras are fundamental in abstract algebra.
  • Elementary functions are widely used in mathematical analysis.
  • D-algebras represent a specific algebraic structure with various applications.

Purpose of the Study:

  • To construct real algebras utilizing elementary functions.
  • To explore the relationship between axioms and conditions for these functions.
  • To establish criteria for real-valued functions to be classified as d-algebras.

Main Methods:

  • Construction of real algebras using a defined set of elementary functions.
  • Analysis of axiomatic relationships and their implications for function properties.
  • Derivation of specific conditions that guarantee a function's d-algebra status.

Main Results:

  • Successful construction of novel real algebras.
  • Identification of key relationships between algebraic axioms and function characteristics.
  • Development of precise conditions for classifying real-valued functions as d-algebras.

Conclusions:

  • Elementary functions can be effectively used to build real algebras.
  • The established conditions provide a clear framework for identifying d-algebras.
  • This work contributes to the understanding of algebraic structures and function theory.