Problem:
In each of the cases below, describe the ring obtained from F2 by adjoining an element x satisfying the relation: (i) x2+x+1=0, (ii) x2+1=0, (iii) x2+x=0.
- Determine if Z/(6) is isomorphic to Z/(2)xZ/(3).
Provide complete and step by step solution for the question and show calculations and use formulas.