I am a beginner, so I don't know much, I know that the melody of a song can be harmonized with chords, and I know how it can be done with 3 note chords and inversions of the chord and the chords with a fourth added note, but in some arrangements that I see, in the background of the song, the 3 notes are played one by one and they would go like,

c - g - c , then d - a - d, basically a note, then a fifth then an octave, for example, in Yiruma's River Flows in You.

I was wondering if these have a name or if they can be substituted with three note major and minor chords, here is an example

http://www.youtube.com/watch?v=y3kDl4dTXss&feature=fvst

Are these broken chords of some kind, what exactly are they?

They are called arpegios.

They are chords played a note at a time.

Yes, they are broken chords.

c-g-c is a C chord and the e (third is dropped)
d-a-d is a D chord and the F# (third is dropped)

The first chord in the video:
notes Gb-Db-Gb is a Gb chord. The "A" in the melody confirms it as Gb minor chord. Then the next chord, D-A-D and A-D in melody is a D chord.

but wait it gets deeper

Actually, you could call all of the above by different names. But, the easiest way (without getting overly convoluted) is to use the lowest note in your bass as the letter name for these chords, as above.

Yes, you can play them differently. But so far most of these chords (in the brief examples above,) have not been confirmed as major or minor. That is, there is no major or minor third to confirm if it is major or minor. I think major though, so minor is going to work so well.

I'm sure, you will get better advice on how to approach this, but hope this gives you something to think about in the meantime.

Thanks a lot for the information.

You're Welcome. Keep up the questions, you will get tons of help out here ... I have