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There are two completely different definitions of Cayley numbers. The first and most commonly encountered type of Cayley number is the eight elements in a Cayley algebra, ...

A more common way to describe a Euclidean ring.

The Cartesian product of a finite or infinite set of modules over a ring with only finitely many nonzero entries in each sequence.

A linear combination of basis quaternions with integer coefficients.

A graph for which every node has finite degree.

An algebra which does not satisfy a(bc)=(ab)c is called a nonassociative algebra.

The only linear associative algebra in which the coordinates are real numbers and products vanish only if one factor is zero are the field of real numbers, the field of ...

Let x:p(x)->xp(x), then for any operator T, T^'=Tx-xT is called the Pincherle derivative of T. If T is a shift-invariant operator, then its Pincherle derivative is also a ...

The l^infty-polynomial norm defined for a polynomial P=a_kx^k+...+a_1x+a_0 by ||P||_infty=max_(k)|a_k|. Note that some authors (especially in the area of Diophantine ...

The contravariant four-vector arising in special and general relativity, x^mu=[x^0; x^1; x^2; x^3]=[ct; x; y; z], (1) where c is the speed of light and t is time. ...