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Saima Anis1, Madad Khan1, Saqib Khan2

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Summary

Researchers introduced a novel nonassociative algebra called left almost algebra. Its genetic properties and relationships with flexible, Jordan, and generalized Jordan algebras were explored.

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Area of Science:

  • Algebraic Structures
  • Nonassociative Algebras

Background:

  • Nonassociative algebras are fundamental in various mathematical fields.
  • Understanding new algebraic structures enhances theoretical frameworks.

Purpose of the Study:

  • Introduce a new nonassociative algebra: left almost algebra.
  • Investigate the fundamental properties of this new algebra.
  • Examine the connections between left almost algebra and other established algebras.

Main Methods:

  • Definition and axiomatic introduction of left almost algebra.
  • Exploration of its inherent algebraic properties.
  • Comparative analysis with flexible, Jordan, and generalized Jordan algebras.

Main Results:

  • Established the existence and basic properties of left almost algebra.
  • Demonstrated its distinct characteristics within the nonassociative algebra landscape.
  • Identified specific relationships and distinctions with flexible, Jordan, and generalized Jordan algebras.

Conclusions:

  • Left almost algebra is a novel and valid mathematical structure.
  • Its properties offer new avenues for research in nonassociative algebra.
  • Further investigation into its applications and theoretical implications is warranted.