A UNIFORM OPEN IMAGE THEOREM FOR l
... is birational to Bn+1 ×Bn ,fn Yn , n ≥ ν. We apply this general construction to the projective system (Xn+1 → Xn )n≥0 in order to show that γn → +∞. Modifying slightly the definition of the projective system (Xn+1 → Xn )n≥0 , our method yields the following unconditional variant of theorem 1.1. Theo ...
... is birational to Bn+1 ×Bn ,fn Yn , n ≥ ν. We apply this general construction to the projective system (Xn+1 → Xn )n≥0 in order to show that γn → +∞. Modifying slightly the definition of the projective system (Xn+1 → Xn )n≥0 , our method yields the following unconditional variant of theorem 1.1. Theo ...
NOETHERIAN MODULES 1. Introduction In a finite
... There is no analogue of Theorem 3.3 for injective ring homomorphisms. For example, R[X] is a Noetherian ring since it’s a PID and the substitution homomorphism f (X) 7→ f (X 2 ) on R[X] is an injective ring homomorphism that is not surjective. Theorem 3.4. If R is a Noetherian integral domain that i ...
... There is no analogue of Theorem 3.3 for injective ring homomorphisms. For example, R[X] is a Noetherian ring since it’s a PID and the substitution homomorphism f (X) 7→ f (X 2 ) on R[X] is an injective ring homomorphism that is not surjective. Theorem 3.4. If R is a Noetherian integral domain that i ...
4. Morphisms
... g. If we assume that I is radical (which is the same as saying that R does not have any nilpotent elements except 0) then X = V (I) is an affine variety in An with coordinate ring A(X) ∼ = R. Note that this construction of X from R depends on the choice of generators of R, and so we can get differen ...
... g. If we assume that I is radical (which is the same as saying that R does not have any nilpotent elements except 0) then X = V (I) is an affine variety in An with coordinate ring A(X) ∼ = R. Note that this construction of X from R depends on the choice of generators of R, and so we can get differen ...
