Under the 'at-will employment' doctrine in the United States, what does an employer generally have the right to do?

At-will employment (the default in most U.S. states) means an employer can terminate an employee for any reason, or no reason, without notice, as long as the termination is not for an illegal reason such as discrimination based on race, gender, religion, age, disability, or retaliation for protected activity like whistleblowing.