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An ideal is a subset I of elements in a ring R that forms an additive group and has the property that, whenever x belongs to R and y belongs to I, then xy and yx belong to I. ...

A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The ...

The prime zeta function P(s)=sum_(p)1/(p^s), (1) where the sum is taken over primes is a generalization of the Riemann zeta function zeta(s)=sum_(k=1)^infty1/(k^s), (2) where ...

Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere ...

As originally stated by Gould (1972), GCD{(n-1; k),(n; k-1),(n+1; k+1)} =GCD{(n-1; k-1),(n; k+1),(n+1; k)}, (1) where GCD is the greatest common divisor and (n; k) is a ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

A connective in logic which yields true if all conditions are true, and false if any condition is false. A AND B is denoted A ^ B (Mendelson 1997, p. 12), A&B, A intersection ...

An addition-multiplication square is a square of integers that is simultaneously a magic square and multiplication magic square. In 1955, Horner found a square of order eight ...

An alternating group is a group of even permutations on a set of length n, denoted A_n or Alt(n) (Scott 1987, p. 267). Alternating groups are therefore permutation groups. ...

The definition of an Anosov map is the same as for an Anosov diffeomorphism except that instead of being a diffeomorphism, it is a map. In particular, an Anosov map is a C^1 ...