My mom has her name as co-inventor on several patents. The company owned everything - she got a nice hand-holdable little lucite commemorative award thingy that embedded the first page of the patent (printed small font) on a small metal plaque.

Pretty much everything that you do on company time and company hardware (office, laptop, network) is owned by them (and can be monitored). There are multiple legal precedents for company ownership/monitoring.

Example of Lucite Mini Patent: http://www.recognizinginnovation.com/miva/merchant.mvc?Scree...