Sql 2005 Trigger - Newbie

I have two tables "Inventory" and "Product". User creates a product then assignes inventory to that product.
The product table and the inventory table both have the same two fields, "GDS" and "prodID" and both share the same field and value of ProductID.
I'm trying to create a trigger for the Inventory table so when the Inventory table has an update or insert,
the values from Product.GDS and Product.prodID values go into the Inventory's record for Inventory.GDS and Inventory.prodID

I an having problems with the trigger as this is my first attempt in creating a trigger.
I have the trigger on the Inventory table and this is what I so far which does not seem to be working, any suggestions (thanks0:


Code:

set ANSI_NULLS ON
set QUOTED_IDENTIFIER ON
go
ALTER TRIGGER [inv]
ON [dbo].[Inventory]
AFTER INSERT,UPDATE
AS
BEGIN
SET NOCOUNT ON;

Update Inventory
Set GDS = i.GDS, prodID = i.prodId
From Inserted i
Inner Join Inventory inv ON i.ProductID = inv.ProductID
END