So, the actual "correct" (i.e. expanded) phrase is :
じゃあ、またね! or じゃまたね!
Keep in mind that is only intended for casual conversations. Other greetings are in order in other contexts (See below). This phrase itself is actually already a shortening where 「じゃ」 replaces 「では」 wit the same meaning but more informal.
To separate it, think of "じゃ「あ」" as then
, "また" is closer to see you
and "ね", albeit more complicated, can be summarized as:
The ね is either implying a question where agreement is expected (...)
So as virmaior pointed out, "また" is probably the closest to see you
. But you would usually use it in a casual way, thus shortening the sentence to either:
That means see you around
, see you soon
...
If you want to be more precise, add an event or a timeframe after また:
- また来週{らいしゅう}! (See you next week)
- また会{あ}おうね! (See you next time we meet)
- また来{き}ます! (I'll be back, lit. see you when I come back)
You can then play around with other durations, and add/remove parts of the original sentence as pointed out in the comments:
- じゃあ、明日{あした}ね (Catch / See you tomorrow)
- また今度{こんど} (Catch / See you next time)
- また後{あと}で (Catch / See you afterwards)
Remember that, as almost always in japanese animation, these are familiar examples (Do not use them in a business context) !