Commutative RingsQ.M.C. (University of London), 1966 - 129 Seiten |
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Ergebnisse 1-3 von 12
Seite 26
... free on elements i then x ; A is S R_ - free S on x / 1 . x ( A ) · and S 2. If A has a finite . free resolution so does Ag = x ( A ) . In particular , this shows that in the commutative case x ( A ) > 0 . S Important special case of ...
... free on elements i then x ; A is S R_ - free S on x / 1 . x ( A ) · and S 2. If A has a finite . free resolution so does Ag = x ( A ) . In particular , this shows that in the commutative case x ( A ) > 0 . S Important special case of ...
Seite 51
... finite resolution hence by Th.4.3 a finite free resolution and applying Th.4.5 ( AB ) we see that the annihilator , viz . M , since it contains no non - zero divisor , must be zero , i.e. , M = 0 and R is a field . Thus unless R is a ...
... finite resolution hence by Th.4.3 a finite free resolution and applying Th.4.5 ( AB ) we see that the annihilator , viz . M , since it contains no non - zero divisor , must be zero , i.e. , M = 0 and R is a field . Thus unless R is a ...
Seite 65
... free resolutions , then the same holds for R ( Just localize ) . 6 . I1 + ( Steinitz ) . I h = J. Let R J1 + S · be ... finite free resolution is principal . complement ) . ( Show by induction on dp ( I ) that I has a free To prove Th ...
... free resolutions , then the same holds for R ( Just localize ) . 6 . I1 + ( Steinitz ) . I h = J. Let R J1 + S · be ... finite free resolution is principal . complement ) . ( Show by induction on dp ( I ) that I has a free To prove Th ...
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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