An argument is very hard on everyone involved. Tempers flare and it's not always easy to stop and listen to what the other person is trying to say.
It's important to remember that there are at least two sides to every argument. And that there are complicated feelings at work on both sides. While you may be feeling that your child isn't recognizing your authority, your child may be feeling she isn't being heard, and that her views and feelings aren't important to you. Both of you are sure to be feeling frustrated and hurt.
It's important to talk about these feelings. Asking the question "Do you feel I'm not listening to you?" may lower the tension level - if you can tolerate an honest response - and, when both of you are less frustrated and feeling better about each other, then it may be possible to negotiate the issue that you disagree about. Encourage listening and discussion instead of arguing, by listening to each other without interrupting, lecturing or scolding.
It often helps to take a break and give everyone a chance to calm down. But if the issue is important, make sure you come back to it soon and resolve it. Acknowledge your child's point of view and try to understand it. Ask yourself: "Does it really matter if we do it his way?" Sometimes you and your child may see things so differently that you have to just agree to disagree (for example, about bedtimes).
If you take your child's point of view seriously, you'll help him feel less defensive, more secure, and maybe even more likely to take your point of view seriously.