Mul[t]iplicative Ideal Theory |
Common terms and phrases
a₁ abelian group algebraic extension Assume Bezout domain cancellation ideal closure completely integrally closed conditions are equivalent convex subgroup Corollary D₁ D₂ Dedekind domain defined denotes direct sum divisor domain with identity domain with quotient Exercise f₁ finitely generated ideal following conditions fractional ideal GCD-domain group of divisibility Hence homomorphism idempotent implies integral domain integrally closed domain intersection invertible isomorphic Krull domain lattice-ordered Lemma M₂ maximal ideal minimal prime monic polynomial Noetherian nonzero element order isomorphic P-primary ideal P₁ partially ordered polynomial positive integer principal ideal PROOF proper ideal proper prime ideal Proposition Prove Prüfer domain quotient field R-module R₂ regular element ring with identity semivaluation set of indeterminates set of maximal set of prime shows subgroup of G subring Theorem total quotient ring totally ordered V₁ valuation ring zero divisors α α λαλελ λελ