This article is a discussion about a ring-theoretic model, which is a math-based model illustrating the mechanism through which intrusion detection is done. Statistically or machine-learned-based detection methods do not necessarily have the structure theory to demonstrate the workings of complex cybersecurity relationships. The proposed model considers system things as the ring elements and the operations of the system such as detection, avoidance, and reaction as the ring operations. Homomorphisms render it secure that systems communicate with each other, and mathematical formulas characterize fake positives and negatives. This is a ring-theory-based approach that helps us comprehend theories more and makes strong and proven attack detection in dynamic cyber environments.