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Different types of Algebra are:

  • Algebra over a field or more generally algebra over a ring.
    Many classes of algebras over a field or over a ring have a specific name:
    • Associative algebra
    • Non-associative algebra
    • Lie algebra
    • Hopf algebra
    • C*-algebra
    • Symmetric algebra
    • Exterior algebra
    • Tensor algebra
  • In measure theory,
    • Sigma-algebra
    • Algebra over a set
  • In category theory
    • F-algebra and F-coalgebra
    • T-algebra
  • In logic,
    • Relational algebra: a set of finitary relations that is closed under certain operators.
    • Boolean algebra, a structure abstracting the computation with the truth values false and true. See also Boolean algebra (structure).
    • Heyting algebra
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