STP question, access switch becoming root

<Cisco Core> VLAN 15 [Root Bridge]            I            |            |            | <Dell N3000>            |            |            |            | <Cisco IE2000> New switch added (VLAN 15 and new VLAN 71)

The whole network is running RSTP. VLAN 15 on my Cisco core is defined as the root switch. Off of my core switch, there is a Dell N3000 trunked. The only STP command defined is on the core- spanning tree vlan 15 priority [#].

Today when I added a new access switch to the Dell, it took over as the Root Bridge for VLAN15. Why would it take over as the root if the priority is defined on my core switch? What should I add to to prevent this from happening, root guard?

Is there a way to stop the access switch from taking over as root?