This is a grammar question in the context of mathematics.
Introduction of the context: I use the word "algebra" here in the sense of a mathematical object (see Algebra over a field (Wikipedia)). Often an algebra is defined over a field K. One then speaks more precisely of a K-algebra or of an algebra over K.
So let K be a field. A K-algebra consists roughly of two things (the details do not matter here):
- a ring R
- a structure that relates it to K
In particular a ring R can become a K-algebra in different ways. So one needs to specify how a given ring R becomes a K-algebra. In such a situation I would write
"We consider R as an algebra over K via ...",
where in "..." I explain the structure that relates R to K.
Question: Should one use the indefinite article "an" in the previous phrase or not? Why?