(algebra, number theory) A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.

(mathematics) A number (real or complex) which is a solution to an equation of the form x²+Bx+C=0 for some integers B and C. For example 42, or 2+3i, or 1+√/2.

plural of algebraic integer

plural of quadratic integer

(algebra) A complex number of the form a+b𝜔, where a and b are integers and ω is defined by the following two rules: (1) 𝜔³=1 and (2) 1+𝜔+𝜔²=0; an element of the Euclidean domain ℤ[𝜔].

plural of Gaussian integer

(mathematics) Any of the scalar products a_ij=2(r_i,r_j)/(r_i,r_i) that make up the Cartan matrix of a simple Lie algebra.

plural of Cartan integer

(mathematics) The decomposition of a composite number into a product of smaller integers

plural of integer factorization