Editing Dual number (section)

==Modern definition==

In modern [[algebra]], the algebra of dual numbers is often defined as the [[quotient ring|quotient]] of a [[polynomial ring]] over the real numbers <math>(\mathbb{R})</math> by the [[principal ideal]] generated by the [[square (algebra)|square]] of the [[indeterminate (variable)|indeterminate]], that is
:<math>\mathbb{R}[X]/\left\langle X^2 \right\rangle.</math>

It may also be defined as the [[exterior algebra]] of a one-dimensional [[vector space]] with <math>\varepsilon</math> as its basis element.