Used other than figuratively or idiomatically: see algebraic, analysis.; the use of techniques from algebra (especially elementary algebra) to analyse and solve problems.

(algebra, combinatorics) A branch of mathematics in which techniques from abstract algebra are applied to problems in combinatorics, and vice versa.

(algebra, mathematical physics) A unital associative algebra which generalizes the algebra of quaternions but which is not necessarily a division algebra; it is generated by a set of 𝛾ᵢ (with i ranging from, say, 1 to n) such that the square of each 𝛾ᵢ is fixed to be either +1 or −1, depending on each i, and such that any product 𝛾ᵢ𝛾ⱼ anticommutes when its factors are distinct (i.e., when i ne j).

(algebra) The branch of mathematics dealing with homology and in particular with homological functors and the algebraic structures they entail.

(mathematics, statistics) A discipline within mathematical statistics in which algebra is used to describe and analyse problems;

plural of Loday algebra

(mathematics) A module over a commutative ring with a bilinear product satisfying the Leibniz identity.

plural of Leibniz algebra

(mathematics) Synonym of Leibniz algebra

(mathematics) The Koszul dual concept to a Leibniz algebra.