Mathematical Modeling for Inherited Diseases

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.