While she slept the alarm kept ringing in Jamie's ear. According to The Elements of Style, what is the correct way to revise this sentence?

According to The Elements of Style, if there is an inversion in a sentence (meaning that the dependent clause is located first, in front of the independent clause), there should be a comma between those two sentences.

So, here is what this sentence should look like:

While she slept, the alarm kept ringing in Jamie's ear.

As you can see, there is a comma after the dependent clause while she slept.