What does it mean to say that a scheme $X$ is simple over $Spec(A)$ ?
I stumbled on this terminology in a paper of S. Lubkin entitled "On a conjecture of Andre Weil".
What does it mean to say that a scheme $X$ is simple over $Spec(A)$ ? I stumbled on this terminology in a paper of S. Lubkin entitled "On a conjecture of Andre Weil". 


I have copied A. Stasinsky's comment who quoted a passage in the introduction of SGA1: "/.../ et de faire un ajustage terminologique, le mot morphisme simple ayant notamment \'et\'e remplac\'e entretemps par celui de morphisme lisse, qui ne pr\^ete pas aux m\^emes confusions." 


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. 

