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Every Lie algebra L is isomorphic to a subalgebra of some Lie algebra A^-, where the associative algebra A may be taken to be the linear operators over a vector space V.

The definition of a set by enumerating its members. An extensional definition can always be reduced to an intentional one. An extension field is sometimes also called simply ...

Let (K,|·|) be a non-Archimedean field. Its valuation ring R is defined to be R={x in K:|x|<=1}. The valuation ring has maximal ideal M={x in K:|x|<1}, and the field R/M is ...

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The Balaban 11-cage is the unique 11-cage graph, derived via a tree excision from the 12-cage graph by Balaban (1973) and proven unique by McKay and Myrvold in 2003. It is ...

Given a point lattice, a cluster is a group of filled cells which are all connected to their neighbors vertically or horizontally.

Model completion is a term employed when existential closure is successful. The formation of the complex numbers, and the move from affine to projective geometry, are ...

Let G be a group and theta n permutation of G. Then theta is an orthomorphism of G if the self-mapping nu of G defined by nu(x)=x^(-1)theta(x) is also an permutation of G.

A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.

The Petersen graph is the cubic graph on 10 vertices and 15 edges which is the unique (3,5)-cage graph (Harary 1994, p. 175), as well as the unique (3,5)-Moore graph. It can ...