Algebraic Structures in Different Disciplines
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
Read more about this topic: Outline Of Algebraic Structures
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