Because a scheme is a locally ringed space X, then it is simple if its topology does not contain a nontrivial two sided ideal. As Spec(A) is referring to the spectrum, this scheme is simple if the set of all proper prime ideals of the noncommutative ring A does not contain any nontrivial two sided ideals defined by x $\cdot$ r $\in$ I, r $\cdot$ x $\in$ I, if the set of ideals (I,+) is a subgroup of an additive group (R,+). In a commutative ring, this is true for all ideals.

Because a scheme is a locally ringed space X, then it is simple if its topology does not contain a nontrivial two sided ideal. As Spec(A) is referring to the spectrum, this scheme is simple if the set of all proper prime ideals of the noncommutative ring A does not contain any nontrivial two sided ideals defined by x $\cdot$ r $\in$ I, r $\cdot$ x $\in$ I, if the set of ideals (I,+) is a subgroup of an additive group (R,+). In a commutative ring, this is true for all ideals in I.