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The kernel of a ring homomorphism f:R-->S is the set of all elements of R which are mapped to zero. It is the kernel of f as a homomorphism of additive groups. It is an ideal ...

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...

Let a general theta function be defined as T(x,q)=sum_(n=-infty)^inftyx^nq^(n^2), then

Let R be a ring, let A be a subring, and let B be an ideal of R. Then A+B={a+b:a in A,b in B} is a subring of R, A intersection B is an ideal of A and (A+B)/B=A/(A ...

A semiring is a set together with two binary operators S(+,*) satisfying the following conditions: 1. Additive associativity: For all a,b,c in S, (a+b)+c=a+(b+c), 2. Additive ...

Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...

A strategy for the iterated prisoner's dilemma in which a prisoner cooperates on the first move, and thereafter copies the previous move of the other prisoner. Any better ...

Transparallel processing refers to this search for regularities in O(2^N) strings as if only one string of length N were concerned (as is possible if the strings form a ...

A vector sum is the result of adding two or more vectors together via vector addition. It is denoted using the normal plus sign, i.e., the vector sum of vectors A, B, and C ...

An odd alternating permutation number, more commonly called an Euler number or secant number.