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Universal algebra studies common properties of all algebraic structures, including groups, rings, fields, lattices, etc. A universal algebra is a pair A=(A,(f_i^A)_(i in I)), ...

A mathematical statement of the equivalence of two quantities. The equality "A is equal to B" is written A=B.

The orthogonal decomposition of a matrix into lower trapezoidal matrices.

The process of finding a reduced set of basis vectors for a given lattice having certain special properties. Lattice reduction algorithms are used in a number of modern ...

The Betti numbers of a compact orientable n-manifold satisfy the relation b_i=b_(n-i).

The relationship x precedes y is written x≺y. The relation x precedes or is equal to y is written x<=y.

The relationship x succeeds (or follows) y is written x≻y. The relation x succeeds or is equal to y is written x>=y.

The term Bol loop refers to either of two classes of algebraic loops satisfying the so-called Bol identities. In particular, a left Bol loop is an algebraic loop L which, for ...

Two elements alpha, beta of a field K, which is an extension field of a field F, are called conjugate (over F) if they are both algebraic over F and have the same minimal ...

A topological space decomposes into its connected components. The connectedness relation between two pairs of points satisfies transitivity, i.e., if a∼b and b∼c then a∼c. ...