Name for condition $A\cap B=\{e\}$ when $A$ and $B$ are algebraic structures

Question

I find in many places of algebra notions like: let $A,B\subset X$ substructures of $X$ (namely subgroups, vector subspaces, etc.) with the property that $A\cap B=\{e\}$, where $e$ is a very special element of the algebraic structure of $X$, namely a neutral element of some operation defined in $X$.

I would like to know if there is a way to name such condition on substructures instead of saying that $A \oplus B$ or something like that. If the question is too broad just take the case that $X$ is a group and $e$ is the neutral element respect to the group operation.

For groups most people say "trivial intersection" (I randomly looked here and found this post for example, and this one). — Dietrich Burde, Apr 25 '23 at 08:39

score 3 · Accepted Answer · answered Apr 25 '23 at 05:04

3

Not sure if this is long enough to be an answer, but from what I've read, saying "$A$ and $B$ trivially intersect" often suffices.

answered Apr 25 '23 at 05:04

IAAW

1,704

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Short answers are the best answers. I think I've also seen it siad that way so you're probably right – David Apr 25 '23 at 07:00

Name for condition $A\cap B=\{e\}$ when $A$ and $B$ are algebraic structures

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