I think it comes from Bourbaki. In french, "compact" is what you call "quasi-compact and Haussdorf". Calling a non-Haussdorf space compact would make no sense hence "quasi-compact".

I imagine it is the same thing for "local = quasi-local + noetherian". For me, a commutative ring is local if it has only one maximal ideal. There is no noetherian hypothesis in the definition.

I think it comes from Bourbaki. In french, "compact" is what you call "quasi-compact and Hausdorff". Calling a non-Hausdorff space compact would make no sense hence "quasi-compact".

I imagine it is the same thing for "local = quasi-local + noetherian". For me, a commutative ring is local if it has only one maximal ideal. There is no noetherian hypothesis in the definition.