SQL MAX of column including its primary key

Question

Short:

From below sql select I get the cart_id and the value of the maximum valued item in that cart.

select CartItems.cart_id, max(ItemValues.value)
from CartItems inner join ItemValues on CartItems.item_id=ItemValues.item_id
group by CartItems.cart_id

but I also need item_id for that item (ItemValues.item-id).

Long:

Two tables, CartItems, ItemValues (and their respective Carts, Items, irrelevant here).
Each cart can have several items wheras each item has one value defined in ItemValues.
Each item belongs to one cart.
The value of a cart is the value of the item with maximum value within its cart.
How do I select cart-id, max(item-value) and it's corresponding item-id?

For instance cart-id A contains item-id X with value 10 and item-id Y with value 90.
With above sql select I get,

A, 90

What I need is

A, Y, 90

platform: MS SQL

Answer 1

In MS SQL and Oracle:

SELECT *
FROM
  (
  SELECT ci.*, iv.*, ROW_NUMBER() OVER (PARTITION BY CartItems.cart_id ORDER BY ItemValues.value DESC)
  FROM   CartItems ci
  INNER JOIN ItemValues iv
     ON CartItems.item_id=ItemValues.item_id
  ) s
WHERE rn = 1

In MySQL:

SELECT
FROM
  (
  SELECT ci.*,
         (
         SELECT id
         FROM ItemValues iv
         WHERE iv.item_id = ci.item_id
         ORDER BY
               value DESC
         LIMIT 1
         ) AS maxitem
  FROM   CartItems ci
  ) iv, ItemValues ivo
WHERE ivo.id = iv.maxitem