How do I know the definition of rings or of anything on the GRE given that definitions can vary? :|
Context is rings:
- A ring with exactly 2 ideals is a field and hence commutative...IF the ring is commutative and thus there are no such notions of right or left ideals I guess.
- I might have incorrectly argued $(s+t)^2=s^2+t^2$ implies $s+s=0$ because I assumed the ring contains $1$.
- If subrings contain 0, then I hope to rule out subsets as subrings if they do not contain 0. I believe this will help me work more quickly in the exam. I don't know if subrings still contain 0 under a different definition of rings. Even if the definition of rings is the same, how do I know the definition of subrings is still the same?
But even outside rings, how do I know that the GRE has the same definition for fields, holomorphic/analytic functions, Hausdorff spaces, uniform continuity or convergence or even rectangles?!