Subjective polynomial maps, and a remark on the jacobian problem.
Submersions and effective descent of étale morphisms
Using the flatification by blow-up result of Raynaud and Gruson, we obtain new results for submersive and subtrusive morphisms. We show that universally subtrusive morphisms, and in particular universally open morphisms, are morphisms of effective descent for the fibered category of étale morphisms. Our results extend and supplement previous treatments on submersive morphisms by Grothendieck, Picavet and Voevodsky. Applications include the universality of geometric quotients and the elimination...
Submodule of free Z-module
In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems - LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this article are described by translating theorems in [11] into theorems of Z-module, however their proofs are...
Submodules of a torsion-free and finitely generated module over a Dedekind ring
Submodules of secondary modules.
Subrings in trigonometric polynomial rings.
Successioni di Gorenstein e proprietà
Sufficient conditions for the Jacobson radical of a commutative ring to contain a prime ideal
Sugli anelli che soddisfano alla condizione topologica di Artin-Rees
Sugli ideali di Borel
In this note we study some algebraic properties of Borel Ideals in the ring of polynomials over an effective field of characteristic zero by using a suitable partial order relation defined on the set of terms of each degree. In particular, in the three variable case, we characterize all the 0-dimensional Borel ideals corresponding to an admissible -vector and their minimal free resolutions.
Sui lemmi di preparazione per gli anelli di serie ristrette
Suites récurrentes et polynômes à plusieurs variables
Sul completato di un anello rispetto ad un ideale di tipo finito
Sul gruppo di Picard degli anelli di serie ristrette e la seminormalità
Sul gruppo di Picard di certi anelli di dimensione 1
Sul polinomio di Hilbert di un modulo graduato
Sulla classificazione dei gruppi analitici commutativi di caratteristica positiva
Sulla henselizzazione degli anelli aritmetici
Sulla Henselizzazione di anelli di valutazione e di anelli di Prüfer
Sulla proprietà di estensione