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Algebraic structures in different disciplines

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description: 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 extensiv ...

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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Algebraic structures in different disciplines

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