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A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...

A pair of consecutive numbers.

Exterior algebra is the algebra of the wedge product, also called an alternating algebra or Grassmann algebra. The study of exterior algebra is also called Ausdehnungslehre ...

The rules for the multiplication of quaternions.

Given a commutative ring R, an R-algebra H is a Hopf algebra if it has additional structure given by R-algebra homomorphisms Delta:H->H tensor _RH (1) (comultiplication) and ...

An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

An operator of period 2, i.e., an operator * which satisfies ((a)^*)^*=a.

A map which is monotone increasing and therefore order-preserving.

The standard Lorentzian inner product on R^4 is given by -dx_0^2+dx_1^2+dx_2^2+dx_3^2, (1) i.e., for vectors v=(v_0,v_1,v_2,v_3) and w=(w_0,w_1,w_2,w_3), ...

The appropriate notion of integer for surreal numbers.