I have read the chapter from the Complex Cobordism.... book of Doug Ravenel.
It is here https://web.math.rochester.edu/people/faculty/doug/mybooks/ravenelA2.pdf.
In the definitions $(A2.1.19)$, page $341$, it is mentioned that-
If $x$ and $y$ are elements in an $R$-algebra $A$ which also "contains the power series $F(x,y)$", let $$x +_F y = F(x,y).$$
This definition seems to be in different language what I know from other sources and $x+_F y=F(x,y)$ is simply giving the group structure.
What does the phrase "contains the power series $F(x,y)$ " mean?
Here $x$ and $y$ are variables from $A$.
I have specifically problem with word $\text{contains}$.
So how does and in what sense $x$ and $y$ $\text{contains}$ the power series $F(x,y)$ ?
It is $A$ which is supposed to contain the power series $F(x,y)$, not $x$ and $y$. That doesn't really clarify much though--what does it mean for $A$ to contain $F(x,y)$? Ravenel seems to be using this phrase in an imprecise informal sense, just saying that $A$ is such that it makes sense to evaluate the infinite sum $F(x,y)$ in $A$. To make this more precise, in practice what he means is that $A$ is complete with respect to some ideal $I$ which contains both $x$ and $y$, so that the power series $F(x,y)$ converges in the $I$-adic topology. For instance, typically $A$ will be something like a power series ring $B[[t]]$ for some $R$-algebra $B$, and $x$ and $y$ will be elements with no constant term so that any power series in $x$ and $y$ converges in the $t$-adic topology.