plural of Azumaya algebra

(algebra) Generically, the arithmetic of matrices, involving matrix addition, scalar multiplication of matrices, matrix multiplication, and matrix inversion.

(algebra) polynomial ring

(algebra) A direct sum with an exterior product of multivector spaces which are all based on a same underlying finite-dimensional vector space. The associative algebra of sums and exterior products of scalars, vectors, blades, multivectors, and hybrid (i.e., non-homogeneous) sums of multivectors of different grades.

(algebra) An algebra over a field; a ring with identity together with an injective ring homomorphism from a field, k, to the ring such that the image of the field is a subset of the center of the ring and such that the image of the field’s unity is the ring’s unity.

plural of Maharam algebra

(mathematics) A complete Boolean algebra having a continuous submeasure (also known as a Maharam submeasure).

(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.

plural of Loday algebra