Artin-Wedderburn theorem states that a ring is semisimple iff it is a finite direct product of matrix rings of division rings. Rotman wrote in his text, Advanced modern algebra, that Wedderburn first proved the above statement for semisimple $k$-algebras where $k$ is a field, then later Artin generalized this as it is stated here, and this is why artinian rings are so called.
I don't get this last sentence. Of course, this might be just the author's opinion so there is no complete answer for this, but the problem is, I don't have any clue why this theorem makes it reasonable to call rings with DCC as artinian rings. What would be a reason?