Can a distributed algorithm be serial? Can  a distributed algorithm be serial? 
For example if I have 3 distinct agents in a network would an algorithm that looks like this be considered a distributed algorithm? 

    Process ABC
       If (you are agentA) then
           Do stuff
       Else if (you are agent B) then
           Wait until agent A has finished doing stuff
           Do other stuff
       Else if (you are agentC) then
           Wait until agent B has finished doing stuff
           Do your own thing
       EndIf
    EndProcess 


To my understanding it should be considered as distributed as long as the agents don't share memory. Wouldn't being serial defeat the purpose of having a distributed algorithm though?
Distributed algorithms are sub-type of parallel algorithm. Different parts of algorithm executes simultaneously on different processors with minimum information sharing and minimum dependency among them. Although the difference between parallel algorithm and distributed algorithm is not very clear but in general parallel algorithm is used for speed-up and increase data handling capacity while distributed algorithm is mainly implemented for fault tolerance, scalability. But in your case, may be you are just storing data in different places (distributed) but the algorithm you are using is not a distributed algorithm.