Me alegra que ellos sean los primeros.
Why is this subjunctive? Is it because it comes after "que"? This sentence doesn't seem to express any doubt about their being the first.
Could I say "me alegra que ser el primero?" if I were talking about myself or would I have to write "me alegra que yo sea el primero"?
you need the subjunctive here because there is "que" but mainly because the main verb is a verb expressing emotion (me alegra que...= I am happy that...); this is what triggers the subjunctive.
Bear in mind that not only the element of doubt is what triggers the subjunctive; there are other scenarios.
Your suggestion "me alegra que ser el primero" wouldn't be correct I am afraid, because you are using "que". You could though drop the "que" and use the infinitive. This would be correct:
Me alegra ser el primero.
Here is a lesson dealing with this. Have a look here. I hope it is useful.
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