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Community microgrids can empower local energy sharing, but the equitable allocation of costs and benefits from shared resources like batteries remains a challenge. Decentralized peer-to-peer trading adds flexibility, yet requires a fair framework to ensure broad participation. Existing frameworks rarely integrate P2P trading with shared battery access and explicit justice-aware cost allocation in a single, coherent design. This gap is especially important where technical efficiency, social legitimacy, and community governance must operate together. This article proposes a decentralized optimization framework that links a P2P trading layer, a battery sharing layer, and a justice-aware cost allocation layer for community microgrids. The framework is designed as a conceptual architecture rather than an empirical or simulation-based study. The framework is constructed conceptually, defining the roles, rules, and interactions of each layer. Decision rules are articulated qualitatively, and evaluation scenarios outline a validation pathway without quantitative simulations. The framework provides a modular architecture where prosumers trade energy directly, a community battery is shared according to contribution-based rules, and costs are allocated using fairness-driven formulas. Three tables summarize the trading mechanisms, justice principles, and evaluation scenarios. The proposed framework can guide the design of equitable and efficient community microgrids, and provides a foundation for future empirical testing and policy development. It emphasizes that decentralized energy systems should be evaluated not only by efficiency, but also by fairness, participation, and social accountability.