Some algebraic structures find uses in disciplines outside of abstract algebra. The following is meant to demonstrate some specific applications in other fields. In Physics: Lie groups are used extensively in physics. A few well-known ones include the orthogonal groups and the unitary groups. Lie algebras Inner product spaces Kac–Moody algebra The quaternions and more generally geometric algebras In Mathematical logic: Boolean algebras are both rings and lattices, under their two operations. Heyting algebras are a special example of boolean algebras. Peano arithmetic Boundary algebra MV-algebra In Computer science: Max-plus algebra Syntactic monoid Transition monoid |

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