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A ring that is commutative under multiplication, has a multiplicative identity element, and has no divisors of 0. The integers form an integral domain.

Given a commutative unit ring R and an extension ring S, an element s of S is called integral over R if it is one of the roots of a monic polynomial with coefficients in R.

An integral embedding of a graph, not to be confused with an integral graph, is a graph drawn such that vertices are distinct points and all graph edges have integer lengths. ...

An equation involving a function f(x) and integrals of that function to solved for f(x). If the limits of the integral are fixed, an integral equation is called a Fredholm ...

A Fredholm integral equation of the second kind phi(x)=f(x)+lambdaint_a^bK(x,t)phi(t)dt (1) may be solved as follows. Take phi_0(x) = f(x) (2) phi_1(x) = ...

An extension ring R subset= S such that every element of S is integral over R.

An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The notion was first ...

The function K(alpha,t) in an integral or integral transform g(alpha)=int_a^bf(t)K(alpha,t)dt. Whittaker and Robinson (1967, p. 376) use the term nucleus for kernel.

The symbol int used to denote an integral intf(x)dx. The symbol was invented by Leibniz and chosen to be a stylized script "S" to stand for "summation."

Let sumu_k be a series with positive terms and let f(x) be the function that results when k is replaced by x in the formula for u_k. If f is decreasing and continuous for ...