Klein 4-ring

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

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 ideal  $\{0,b\}$.

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