Editing Primitive ring (section)

==Properties==
One-sided primitive rings are both [[semiprimitive ring]]s and [[prime ring]]s.  Since the [[product ring]] of two or more nonzero rings is not prime, it is clear that the product of primitive rings is never primitive.  

For a left [[Artinian ring]], it is known that the conditions "left primitive", "right primitive", "prime", and "[[simple ring|simple]]" are all equivalent, and in this case it is a [[semisimple ring]] isomorphic to a square [[matrix ring]] over a division ring.  More generally, in any ring with a minimal one sided ideal, "left primitive" = "right primitive" = "prime".

A [[commutative ring]] is left primitive if and only if it is a [[field (mathematics)|field]].

Being left primitive is a [[Morita equivalence|Morita invariant property]].