TITLE: Is there a term for two subsets whose intersection is {0}?
QUESTION [7 upvotes]: In linear algebra I've just recently learned about the "direct sum", which can be defined as the sum of two vector spaces whose intersection is the null vector. 
Basically, I'm wondering if there's a formal term in abstract algebra to define algebraic substructures whose intersection is the identity element, as it seems like it'd be a, in the case of vector spaces, useful way to differentiate between subspaces that can be directly summed and subspaces that can't be.
I'm specifically asking this because algebraic substructures whose intersection is the identity element seem like they could have some interesting interacting properties that differ from the interacting properties of any two substructures (and that the term disjoint wouldn't work in the case of any algebraic substructures).

REPLY [2 votes]: In the context of subspaces of a vector space (or more generally, subgroups of a group), it is common to abuse terminology and call such subspaces disjoint.  This abuse is generally harmless since it is obviously impossible for them to actually be literally disjoint.  You could also call them (linearly) independent, though personally I think "disjoint" sounds much more natural.  I would not, however, use either term to describe arbitrary subsets (as opposed to subspaces) of a vector space whose intersection is $\{0\}$.