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A natural transformation Phi={Phi_C:F(C)->D(C)} between functors F,G:C->D of categories C and D is said to be a natural isomorphism if each of the components is an ...

A group G is nilpotent if the upper central sequence 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... of the group terminates with Z_n=G for some n. Nilpotent groups have the property that ...

The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another equivalent description is that it is the intersection of the prime ...

A positive value of n for which x-phi(x)=n has no solution, where phi(x) is the totient function. The first few are 10, 26, 34, 50, 52, ... (OEIS A005278).

A nonempty set is a set containing one or more elements. Any set other than the empty set emptyset is therefore a nonempty set. Nonempty sets are sometimes also called ...

A positive even value of n for which phi(x)=n, where phi(x) is the totient function, has no solution. The first few are 14, 26, 34, 38, 50, ... (OEIS A005277).

Let A be a C^*-algebra, then an element a in A is called normal if aa^*=a^*a.

In every residue class modulo p, there is exactly one integer polynomial with coefficients >=0 and <=p-1. This polynomial is called the normal polynomial modulo p in the ...

A normal series of a group G is a finite sequence (A_0,...,A_r) of normal subgroups such that I=A_0<|A_1<|...<|A_r=G.

A sequence of n 0s and 1s is called an odd sequence if each of the n sums sum_(i=1)^(n-k)a_ia_(i+k) for k=0, 1, ..., n-1 is odd.