Commutativity of Rings |
Common terms and phrases
a₁ a²p(a ab-ba absolutely algebraic algebraic closure algebraic over F an(a characteristic p0 contains contradiction Corollary Dedekind domain Definition Let division ring element a ɛ exists an element exists an integer exists p(a f₁ finite field finite number finitely many elements Hence implies infinite integer integral domain integrally closed irreducible polynomial isomorphic K-ring Lemma Lemma III Let F m-system minimal ideal minimum polynomial natural number nil ideal nilpotent elements non-equivalent non-trivial valuations non-unit non-zero elements non-zero radical number of prime P₁ pick prime field prime ideal primitive rings proper prime ideals Proposition proved quotient field R/N is commutative ring with center satisfies Step subdirect sum subdirectly irreducible ring subring Suppose Theorem 22 transcendence basis transcendental over F two-sided ideal v₁ v₂ valuation defined YC-W z(ab zero divisor zero radical ε Ζ εθ