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The kernel of a module homomorphism f:M-->N is the set of all elements of M which are mapped to zero. It is the kernel of f as a homomorphism of additive groups, and is a ...

A mathematical object which consists of a set of a single element, making it a 1-tuple. The yin-yang is also known as the monad.

For a given n, is the problem of determining if a set is mortal solvable? n=1 is solvable, n=2 is unknown, and n>=3 is unsolvable.

The set of elements g of a group such that g^(-1)Hg=H, is said to be the normalizer N_G(H) with respect to a subset of group elements H. If H is a subgroup of G, N_G(H) is ...

A game for which each player has a different set of moves in any position. Every position in an impartial game has a nim-value.

The homeomorphic image of a so-called "complete separable" metric space. The continuous image of a Polish space is called a Souslin set.

A premise is a statement that is assumed to be true. Formal logic uses a set of premises and syllogisms to arrive at a conclusion.

A relation "<=" is called a preorder (or quasiorder) on a set S if it satisfies: 1. Reflexivity: a<=a for all a in S. 2. Transitivity: a<=b and b<=c implies a<=c. A preorder ...

An Abelian planar difference set of order n exists only for n a prime power. Gordon (1994) has verified it to be true for n<2000000.

The two-dimensional space consisting of the set of triples {(a,b,c):a,b,c in K, not all zero}, where triples which are scalar multiples of each other are identified.