Klein 4-ring

One of the two smallest non-commutative rings is the Klein 4-ring(R,+,)  where  (R,+)  is the Klein 4-group{0,a,b,c}  with 0 the neutral element and the binary operationMathworldPlanetmath” given by the table

0abc 00000a0a0ab0b0bc0c0c

Note that this ring has two different right unities a and c.

The Klein 4-ring has the subrings{0,a},  {0,b}  and  {0,c}  and the two-sided idealMathworldPlanetmath{0,b}.

Title Klein 4-ring
Canonical name Klein4ring
Date of creation 2015-06-04 16:11:18
Last modified on 2015-06-04 16:11:18
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 16
Author pahio (2872)
Entry type Definition
Classification msc 20-00
Classification msc 16B99
Synonym Klein’s four-ring
Synonym Klein four-ring
Related topic Klein4Group
Related topic InversesInRings
Related topic NonCommutativeRingsOfOrderFour
Related topic GroupsInField
Related topic Subcommutative