Clearly it must be (left) noetherian! (Since we wouldn’t want a ascending subnormal chain that doesn’t stop where all of the elements are enjoyed by the larger ideals/submodules) :)
Sorry, writing “R is comm(unitive)” so many times can make you do things
I’m so tired of transcendental apologists; their lack of a minimal polynomial does NOT permit them to act like this. ϕ was our compromise