Inventory client side ? what do you mean the HUD part ? OFC it is client side
The DATA part, the information of your inventory should be Server side… In my opinion you are free to do it however you want.
Remember the server is like the god manipulating and the clients just mortals : P Stupid example I know but hey it works.
Once the mortal dies, the server should know what items the client has to show the items on floor to the other mortals Clients…
If only mortal knows and can manipulate em then he can cheat easily… well I am no hacker but come on it is way easier to manipulate your computer than 1000 KM away computer. AKA server