non-commutative rings of order four

Up to isomorphismPlanetmathPlanetmathPlanetmathPlanetmath, there are two non-commutative rings of order ( four. Since all cyclic rings are commutativePlanetmathPlanetmath (, one can immediately deduce that a ring of order four must have an additive groupMathworldPlanetmath that is isomorphic to 𝔽2𝔽2.

One of the two non-commutative rings of order four is the Klein 4-ring, whose multiplication table is given by:


The other is closely related to the Klein 4-ring. In fact, it is anti-isomorphic to the Klein 4-ring; that is, its multiplication table is obtained by swapping the of the multiplication table for the Klein 4-ring:

Title non-commutative rings of order four
Canonical name NoncommutativeRingsOfOrderFour
Date of creation 2013-03-22 17:09:24
Last modified on 2013-03-22 17:09:24
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 12
Author Wkbj79 (1863)
Entry type Topic
Classification msc 20-00
Classification msc 16B99
Related topic Klein4Ring
Related topic OppositeRing
Related topic ExampleOfKlein4Ring