What is the different between Classical,Long Run and Short run quantity theory of money(QTM)?

I have read that the transaction demand for money(Mt)is defined as kPY, where k=1/velocity of circulation. However, the book also defined Money demand(Md)=kPY for the derivation of QTM. As we know, Md consists of both Mt and asset demand for money(Ma), so which one is true ,Mt=kPY or Md = kPY?

I have also read that in the long run Mt = Md(i.e.Ma=0),does "Mt=kPY" holds only in LR?

Thank you very much


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