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- Elementary algebra — symbolic arithmetic and its application to solving equations
- Intermediate algebra — first study of functions, relations and graphs
- Abstract algebra — axiomatic study of algebraic structures such as groups, rings and fields
- Linear algebra — vectors, tensors and matrices
- Universal algebra — study of characteristics common to all of the above
An algebra is generally a mathematical space that obeys certain properties. This includes:
- Algebra over a field (and associative algebra)
- Algebra over a commutative ring
- Algebra over a set (and sigma algebra)
- Also an algebra is a vector space with a multiplication inter vectors. Here, belongs the famous Lie's algebras