Solving the Wheel Problem: A Conservative Extension of ℝ with Invertible Division by Zero

Key Points

• The aim is to construct a new algebraic system where division by zero is invertible while maintaining essential arithmetic properties.
• Developed a layered algebra extending real numbers through finitely supported convolution algebras.
• Preserved arithmetic properties such as commutativity, associativity, and distributivity during construction.
• Introduced a projection homomorphism to map onto an extended real structure.
• Successfully differentiated distinct quantities divided by zero, preventing the collapse found in traditional wheel structures.
• Maintained foundational algebraic properties in the new algebraic framework.