Contributed to the CohenMacaulay and mathlib4 repositories by developing advanced formalizations in commutative algebra using Lean. Focused on localized modules, linear equivalences, and associated primes, the work introduced new modules and lemmas that clarified the behavior of mappings under localization and strengthened the robustness of algebraic proofs. Enhanced the Algebra module in mathlib4 by implementing localization equivalence for finitely presented modules, enabling more precise reasoning about S^{-1}-based constructions. Leveraged skills in abstract algebra, category theory, and formal verification to deliver foundational features that support future extensions and higher-level abstractions in formalized mathematics, with an emphasis on correctness and maintainability.