On Two Conjectures About Polynomial Rings.
On two-dimensional regular local rings and a lifting problem
On unimodular complements
On unique and almost unique factorization of complete ideals II.
On valuation spectra
On z◦ -ideals in C(X)
An ideal I in a commutative ring R is called a z°-ideal if I consists of zero divisors and for each a ∈ I the intersection of all minimal prime ideals containing a is contained in I. We characterize topological spaces X for which z-ideals and z°-ideals coincide in , or equivalently, the sum of any two ideals consisting entirely of zero divisors consists entirely of zero divisors. Basically disconnected spaces, extremally disconnected and P-spaces are characterized in terms of z°-ideals. Finally,...
On Zariski-regularity, the vanishing of Tor and a uniform Artin-Rees theorem
On zero-dimensional subschemes of a complete intersections.
One-Dimensional Local Rings with Reduced Associated Graded Ring and Their Hilbert Functions.
One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal
Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate quadratic...
Openly embedding local noetherian domains.
Opération de Cartier et vecteurs de Witt
Opérations sur l'homologie cyclique des algèbres commutatives.
Optimal Betti numbers of forest ideals.
Order complex of ideals in a commutative ring with identity
Order complex is an important object associated to a partially ordered set. Following a suggestion from V. A. Vassiliev (1994), we investigate an order complex associated to the partially ordered set of nontrivial ideals in a commutative ring with identity. We determine the homotopy type of the geometric realization for the order complex associated to a general commutative ring with identity. We show that this complex is contractible except for semilocal rings with trivial Jacobson radical when...
Ordered fields.
Orderings of Higher Level and Semilocal Rings.
Orderings of monomial ideals
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular, we give an interpretation of the height function in terms of the Hilbert-Samuel polynomial, and we compute bounds on the maximal order type.
Ordres de Gorenstein
Ordres faibles et localisation de zéros de polynômes