Editing Digroup (section)

{{about|the algebraic structure|telecommunications|Digital multiplex hierarchy}}

In the mathematical area of [[algebra]], a '''digroup''' is a generalization of a [[Group (mathematics)|group]] that has two one-sided product operations, <math>\vdash</math> and <math>\dashv</math>, instead of the single operation in a group.  Digroups were introduced independently by Liu (2004), Felipe (2006), and Kinyon (2007), inspired by a question about [[Leibniz algebra]]s.

To explain digroups, consider a group. In a group there is one operation, such as addition in the set of integers; there is a single "unit" element, like 0 in the integers, and there are inverses, like <math>-x</math> in the integers, for which both the following equations hold: <math>(-x)+x=0</math> and <math>x+(-x)=0</math>.  A digroup replaces the one operation by two operations that interact in a complicated way, as stated below.  A digroup may also have more than one "unit", and an element <math>x</math> may have different inverses for each "unit".  This makes a digroup vastly more complicated than a group.  Despite that complexity, there are reasons to consider digroups, for which see the references.