Commutative RingsQ.M.C. (University of London), 1966 - 129 Seiten |
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Ergebnisse 1-3 von 8
Seite 22
... exact sequence OK BF → 0 with F free splits ; for we can map the free generators of F back to B and extend this to a homomorphism . The precise class of modules with this property can be ... short exact sequences 22 Finite resolutions.
... exact sequence OK BF → 0 with F free splits ; for we can map the free generators of F back to B and extend this to a homomorphism . The precise class of modules with this property can be ... short exact sequences 22 Finite resolutions.
Seite 23
Irving Kaplansky. Lemma ( Schanuel ) . Given two short exact sequences 0 → K✦ PA 0 , → 0 + V + 0 → K1 → P where PoP1 are projective , then KO P K + F. 1 Proof . Let L = { ( p , p ' ) & P F2 | fp gp ' } ( pullback ' , PK1 to L b lift ...
Irving Kaplansky. Lemma ( Schanuel ) . Given two short exact sequences 0 → K✦ PA 0 , → 0 + V + 0 → K1 → P where PoP1 are projective , then KO P K + F. 1 Proof . Let L = { ( p , p ' ) & P F2 | fp gp ' } ( pullback ' , PK1 to L b lift ...
Seite 73
... short exact sequences , where modules with FFR of length < k . ( as in Schanuel's Lemma ) . Thus B , C , D , E are torsion Form the pullback of f and В W = set of all ( b , d ) with f ( b ) 8 g ( d ) . Then W is a torsion module with ...
... short exact sequences , where modules with FFR of length < k . ( as in Schanuel's Lemma ) . Thus B , C , D , E are torsion Form the pullback of f and В W = set of all ( b , d ) with f ( b ) 8 g ( d ) . Then W is a torsion module with ...
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Häufige Begriffe und Wortgruppen
A/xA algebraic annihilator assume Auslander-Buchsbaum chains of prime co-dimension coefficients commutative ring complete the proof contains a non-zero contradiction Corollary Dedekind ring defined Definition dimension direct summand discrete valuation ring elements Exercise exists Ext A,B finite free resolution finite number finitely generated R-module follows free module G-ideal G-ring Given grade hence Hilbert ring homomorphism hypothesis ideal contains induction integral domain integrally closed intersection invertible ideal Krull Lemma little rank Macaulay ring maximal chain maximal ideal maximal R-sequence minimal prime ideal Noetherian ring non-zero divisor Note P₁ P₁U polynomials principal ideal theorem principal prime projective prove Prüfer ring quotient field R-free R-projective rank Q regular local n-dimensional regular local ring result ring with quotient short exact sequences submodule subring torsion modules write x₁ zero zero-divisors χε