| Structure | Associativity | Identity | Inverse | Commutativity | Abelian group under + | Distributivity | No zero divisors | Idempotence (·) | Invertibility of nonzero elements | char > 0 | Total order (≤) | Dense order | Discrete order | Typical examples |
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| Structure | Commutativity (∧,∨) | Associativity (∧,∨) | Idempotence (∧,∨) | Absorption (∧,∨) | Modularity | Distributivity | Boundedness (0,1) | Complement (a') | Uniqueness of a' | Completeness (⋀S,⋁S) | Atomicity | Partial order (≤) | Linearity (chain) | Typical examples |
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