Understanding of Definition of Field Homomorphism

Question

Let $(F,+,.)$ and $(K,\oplus,\odot)$ be two fields. The map $f:F\rightarrow K$ is called field homomorphism, if for all $a,b\in F:$

$f\left( a+b\right) =f\left( a\right) \oplus f\left(b\right)$,

$f\left( a.b\right) =f\left( a\right)\odot f\left( b\right)$.

My question is:What is difference between $+$ and $\oplus$ also, $.$ and $\odot$?

Answer 1

$+$ is a binary operation on $F$ such that $(F,+)$ forms an abelian additive group.

$\oplus$ is a binary operation on $K$ such that $(K,+)$ forms an abelian additive group.

Similarly $\odot$ is a binary operation on $K$ such that $(K\setminus\{0\},\odot)$ forms an abelian multiplicative group.

$.$ is a binary operation on $K$ such that $(F\setminus\{0\},.)$ forms an abelian multiplicative group.