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- Algebra (ring theory)
- Algebra over a field
- Nilpotent algebra (ring theory)
- *-algebra
- Affine Hecke algebra
- Algebra homomorphism
- Algebra representation
- Associative algebra
- Augmentation (algebra)
- Azumaya algebra
- Batalin–Vilkovisky formalism
- Beurling algebra
- Bracket algebra
- CCR and CAR algebras
- Cellular algebra
- Central simple algebra
- Colombeau algebra
- Composition algebra
- Derivative algebra (abstract algebra)
- Difference algebra
- Differential graded algebra
- Division algebra
- Double affine Hecke algebra
- Duffin–Kemmer–Petiau algebra
- Exterior algebra
- Filtered algebra
- Finitely generated algebra
- Fourier algebra
- Fréchet algebra
- Free algebra
- Frobenius algebra
- Frobenius theorem (real division algebras)
- Functional-theoretic algebra
- Generalized Clifford algebra
- Gerstenhaber algebra
- Graded ring
- Group algebra
- Hall algebra
- Hurwitz quaternion order
- Iwahori–Hecke algebra
- Koszul algebra
- Koszul duality
- List of algebras
- Max-plus algebra
- Normed algebra
- Partial group algebra
- Peak algebra
- Peirce decomposition
- Poisson algebra
- Pseudo-ring
- Quadratic algebra
- Quaternion algebra
- R-algebroid
- 2 × 2 real matrices
- Rng (algebra)
- Rota–Baxter algebra
- Semisimple algebra
- Separable algebra
- Simple algebra
- Superalgebra
- Supercommutative algebra
- Symmetric algebra
- Tensor algebra
- Tensor product of algebras
- Ternary commutator
- Topological algebra
- Weyl algebra