TITLE: Looking for the name of a definition
QUESTION [0 upvotes]: If I have a set that ordered, where you can add / subtract scalar values to but cannot multiply /divide against them, what is the set called? Is it just ordered?

REPLY [2 votes]: I think you mean a linearly ordered Abelian group.
This is just an Abelian group $(G,+,-,0)$, with a linear order $\le$ such that 
the group structure and the order behave nicely together:

$\forall g,h, k \in G : g \le h \rightarrow g+ k \le h +k$
$\forall g,h \in G: g \le h \rightarrow -h \le -g$.

You can also generalise to just groups and partial orders (e.g. ordered topological vector spaces etc.) See wikipedia  e.g.
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