List of algebras
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).
- *-algebra
 - Affine Lie algebra
 - Akivis algebra
 - Algebra for a monad
 - Albert algebra
 - Alternative algebra
 - AW*-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
 - Functional-theoretic algebra
 - Genetic algebra
 - Geometric algebra
 - Gerstenhaber algebra
 - Graded algebra
 - Griess algebra
 - Group algebra
 - Group algebra of a locally compact group
 - 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
 - Matrix algebra
 - Non-associative algebra
 - Octonion algebra
 - Pre-Lie algebra
 - Poisson algebra
 - Process algebra
 - Quadratic algebra
 - Quaternion algebra
 - Rees algebra
 - Relation algebra
 - Relational algebra
 - Rota–Baxter 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
 - Weyl algebra
 - Zinbiel algebra
 
This is a list of fields of algebra.