Please Login to access more options.
Problem 1 (Listing The Properties Of A Field)
Suppose that $F$ is a field. Since $(F,+)$ and $(F^*,\cdot)$ are Abelian group, this means there are several properties that the binary operations $+$ and $*$ must satisfy. Make a list of all these properties, which together with the distributive laws, should give you a list of 9 properties that characterize a field. Then state at least two other sets that you know satisfy these properties.
The following pages link to this page.