This is a list of possibly nonassociative algebras. An algebra is a module, wherein you can also multiply two module elements. (The multiplication in the module is compatible with multiplication-by-scalars from the base ring).

Akivis algebra

Algebra for a monad

Albert algebra

Alternative algebra

Azumaya algebra

Banach algebra

Birman–Wenzl algebra

Boolean algebra

Borcherds algebra

Brauer algebra

C*-algebra

Central simple algebra

Clifford algebra

Cluster algebra

Dendriform algebra

Differential graded algebra

Differential graded Lie algebra

Exterior algebra

F-algebra

Filtered algebra

Flexible algebra

Freudenthal algebra

Genetic algebra

Geometric algebra

Gerstenhaber algebra

Graded algebra

Griess algebra

Group algebra[disambiguation needed]

Hall algebra

Hecke algebra of a locally compact group

Heyting algebra

Hopf algebra

Hurwitz algebra

Hypercomplex algebra

Incidence algebra

Iwahori–Hecke algebra

Jordan algebra

Kac–Moody algebra

Kleene algebra

Leibniz algebra

Lie algebra

Lie superalgebra

Malcev algebra

Non-associative algebra

Octonion algebra

Pre-Lie algebra

Poisson algebra

Process algebra

Quadratic algebra

Quaternion algebra

Rees algebra

Relation algebra

Relational algebra

Schur algebra

Semisimple algebra

Separable algebra

Shuffle algebra

Sigma-algebra

Simple algebra

Structurable algebra

Supercommutative algebra

Symmetric algebra

Tensor algebra

Universal enveloping algebra

Vertex operator algebra

von Neumann algebra

Zinbiel algebra

This is a list of fields of algebra.

Linear algebra

Homological algebra

Universal algebra

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Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

Hellenica World - Scientific Library

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