non-commutative rings of order four
Up to isomorphism, there are two non-commutative rings of order (http://planetmath.org/OrderRing) four. Since all cyclic rings are commutative (http://planetmath.org/CommutativeRing), one can immediately deduce that a ring of order four must have an additive group that is isomorphic to .
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|
|Date of creation||2013-03-22 17:09:24|
|Last modified on||2013-03-22 17:09:24|
|Last modified by||Wkbj79 (1863)|