By Hopkins Theorem it is well-known that every right (resp. left) artinian ring is right (left) noetherian. Suppose that a noncommutative ring R satisfies the descending chain condition on its two-sided ideals. Does R satisfy the ascending chain condition on two-sided ideals?

By Hopkins Theorem it is well-known that every right (resp. left) artinian unitary ring is right (left) noetherian. Suppose that a noncommutative unitary ring R satisfies the descending chain condition on its two-sided ideals. Does R satisfy the ascending chain condition on two-sided ideals?

By Hopkins Theorem it is well-known that every right (resp. left) artinian ring is right (left) noetherian. Suppose that a noncommutative ring R satisfies the descending chain condition on its two-sided ideal. Does R satisfy the ascending chain condition on two-sided ideals?

By Hopkins Theorem it is well-known that every right (resp. left) artinian ring is right (left) noetherian. Suppose that a noncommutative ring R satisfies the descending chain condition on its two-sided ideals. Does R satisfy the ascending chain condition on two-sided ideals?