On Algebraic Integral

Key Points

• The aim is to extend integration concepts to monoid actions and classify regular integrals along with developing new methods.
• Generalization of the integration concept to monoid actions.
• Establishment of a representation for regular integrals through bijective crossed-homomorphisms.
• Classification of regular integrals over the real numbers.
• Successful establishment of a framework for representing regular integrals.
• Complete classification of regular integrals is achieved.
• Development of a novel algebraic method of integration.