# “as an algebra” or “as algebra” (zero article or indefinite article)?

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?

In the structured phrase `we consider X to be Y`, the term `Y` is read as a property of `X`. E.g.: we consider an apple to be edible.
In your example, you're saying that `X` is one of potentially several kinds of `Y`, so an indefinite article is used. E.g.: we consider an apple to be a fruit.