Not only can the employer terminate you, but if there is a company rule against using the computer for nonbusiness reasons, you may have problems getting unemployment benefits.
The reason for this is that the computer, its software, and the access to the Internet are all considered to be company property. Many employers consider using their computers for an employee’s own purpose a form of stealing. Additionally, you are being paid to work and do the assignments for the employer.
Many employers are now monitoring the websites that their employees access during work hours to make sure they are doing work. This is not against the law; in fact, the courts have specifically allowed employers to do this.