Multiplicative Ideal Theory |
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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 maximal ideal minimal prime monic polynomial multiplicative system Noetherian nonzero element order isomorphic P-primary ideal partially ordered polynomial positive integer principal ideal PROOF proper ideal proper prime ideal Proposition Prove Prüfer domain quotient field R-module R₂ rank one discrete 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 valuation ring α α λελ
References to this book
Computational Methods in Commutative Algebra and Algebraic Geometry Wolmer Vasconcelos Limited preview - 2004 |
Relative Homological Algebra, Volume 1 Edgar E. Enochs,Overtoun M. G. Jenda No preview available - 2000 |