Is the term "Spans Unity" common?

Question

I recently saw a definition in a paper I haven't seen before. Given a commutative ring with identity $R$ and a subset $X$, we say $X$ spans unity in $R$ if there exist $a_1,...,a_n\in X$ and $\lambda_1,...,\lambda_n\in R$ such that $1=\sum_{i=1}^n\lambda_i a_i$. It's easy to verify that this is equivalent to saying the ideal generated by $X$ is $R$. More generally, given another subset $Y$, we say $X$ spans unity in $R$ with coefficients from $Y$ if there exist $a_1,...,a_n\in X$ and $\lambda_1,...,\lambda_n\in Y$ such that $1=\sum_{i=1}^n\lambda_i a_i$. Is this terminology common practice?

Answer 1

I have not seen this term before, and it gets rather few hits on Google, most of which appear to not be about math. The more common term for this in my experience is "generates the unit ideal" (which gets almost 20 times as many hits, almost all of which are relevant).

I don't know a more standard way to say "$X$ spans unity in $R$ with coefficients in $Y$", and the ability to neatly express this concept may be the reason that the authors chose to use the unusual terminology "spans unity".