User:Nwbeeson/sandbox/MathRingInfobox

Ring and field axioms   Ring Commutative ring Skew field or Division ring Field Abelian (additive) group structure Yes Yes Yes Yes Multiplicative structure and distributivity Yes Yes Yes Yes Commutativity of multiplication No Yes No Yes Multiplicative inverses No No Yes Yes

Fields

+	O	I	A	B
O	O	I	A	B
I	I	O	B	A
A	A	B	O	I
B	B	A	I	O

·	O	I	A	B
O	O	O	O	O
I	O	I	A	B
A	O	A	B	I
B	O	B	I	A