On the structure of Noetherian symbolic Rees Algebras.
On the Symmetric Algebra of an Ideal.
On the uniform behaviour of the Frobenius closures of ideals
Let be a proper ideal of a commutative Noetherian ring R of prime characteristic p and let Q() be the smallest positive integer m such that , where is the Frobenius closure of . This paper is concerned with the question whether the set is bounded. We give an affirmative answer in the case that the ideal is generated by an u.s.d-sequence c₁,..., cₙ for R such that (i) the map induced by multiplication by c₁...cₙ is an R-monomorphism; (ii) for all , c₁/1,..., cₙ/1 is a -filter regular sequence...
On unique and almost unique factorization of complete ideals II.
On wsq-primary ideals
We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let be a commutative ring with a nonzero identity and a proper ideal of . The proper ideal is said to be a weakly strongly quasi-primary ideal if whenever for some , then or Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional...
On Zariski-regularity, the vanishing of Tor and a uniform Artin-Rees theorem
Polynôme d'Hilbert-Samuel des clôtures intégrales des puissances d'un idéal m-primaire
Polynomes à valeurs entières sur un anneau non analytiquement irréductible.
Polynomial rings over pseudovaluation rings.
Polynomials with high multiplicity
Premiers, copremiers et fibrés
Primary elements in Prüfer lattices
In this paper we study primary elements in Prüfer lattices and characterize -lattices in terms of Prüfer lattices. Next we study weak ZPI-lattices and characterize almost principal element lattices and principal element lattices in terms of ZPI-lattices.
Primary ideals with finitely generated radical in a commutative ring.
Prime ideals in universal algebras
Prime, weakly prime and almost prime elements in multiplication lattice modules
In this paper, we study multiplication lattice modules. We establish a new multiplication over elements of a multiplication lattice module.With this multiplication, we characterize idempotent element, prime element, weakly prime element and almost prime element in multiplication lattice modules.
Principal ideal theorems for holomorphy rings in fields.
Pseudobetragsfunktionen auf Quotientenkörpern von Dedekindringen.
Pseudo-valuation rings. II
Viene data una condizione sufficiente affinchè un sopra-anello di un anello di pseudo-valutazione (PVR) sia ancora un PVR. Da ciò segue che se è un PVR, allora ogni sopra-anello di è un PVR se (e soltanto se) è quasi-locale per ciascun elemento di . Vari risultati sono dimostrati per un ideale primo di un anello commutativo arbitrario , avente come insieme di zero-divisori. Per esempio, se è un primo «forte» di e contiene un elemento non-zero divisore di , allora è un sopra-anello...
Pure submodules of multiplication modules.
Quantum entanglement and projective ring geometry.