Fields When to Use Use this skill when working on fields problems in abstract algebra. Decision Tree 1. Is F a field? - (F, +) is an abelian group with identity 0 - (F \ {0}, ) is an abelian group with identity 1 - Distributive law holds - 2. Field Extensions - E is extension of F if F is subfield of E - Degree [E:F] = dimension of E as F-vector space - for minimal polynomial 3. Characteristic - char(F) = smallest n 0 where n 1 = 0, or 0 if none exists - char(F) is 0 or prime - For finite field: |F| = p^n where p = char(F) 4. Algebraic Elements - alpha is algebraic over F if it satisfies poly…