Design a backend architecture of a new material ordering system for an e-commerce company. The service will be implemented in C# using the ASP.NET Core framework. Analyze the system requirements and design an architecture based on these needs, applying Domain-Driven Design principles. Discuss your decisions and provide a rationale for your choices. Then, implement a basic project that demonstrates the proposed solution.

The existing implementation uses a traditional n-layer architecture for its product ordering system. Compare the proposed architecture with the existing solution, highlighting the improvements and benefits of the new design. Additionally, the system must ensure the auditability of processes. The goal is to design a solution that enables developers to trace back the actions performed within the application. For certain processes, it is also desirable for users to see the history through the UI. Evaluate potential approaches and select the most appropriate solution.