This paper describes an algebraic approach to the security engineering of lattice policies. The approach extends earlier lattice and algebraic work, and has two main goals. First, it seeks to model access control policies with anti-symmetry, reflexivity and transitivity exceptions using a lattice, and to propose an information flow security definition for the resulting set (POL) of policies. Second, it supports a constructive approach to policy specification through an algebraic structure (POL, AND, OR, NOT, =, <). This structure is homomorphic to Boolean algebra. The approach's goals and design decisions are influenced by the context in which it is being used: a library of reusable security components with tools to facilitate their reuse for securing application systems.