On the Regularity of Graded k-Algebras of Krull Dimension ...1.
On the stable equivalence problem for k[x,y]
L. Makar-Limanov, P. van Rossum, V. Shpilrain and J.-T. Yu solved the stable equivalence problem for the polynomial ring k[x,y] when k is a field of characteristic 0. In this note we give an affirmative solution for an arbitrary field k.
On the structure of linear recurrent error-control codes
We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.
On the structure of linear recurrent error-control codes
We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.
On the structure of Noetherian symbolic Rees Algebras.
On the structure of the canonical model of the Rees algebra and the associated graded ring of an ideal.
In this note we give a description of a morphism related to the structure of the canonical model of the Rees algebra R(I) of an ideal I in a local ring. As an application we obtain Ikeda's criteria for the Gorensteinness of R(I) and a result of Herzog-Simis-Vasconcelos characterizing when the canonical module of R(I) has the expected form.
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 the Weierstrass division.
On the zero set of semi-invariants for quivers
On unique and almost unique factorization of complete ideals II.
On valuation spectra
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 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
Openly embedding local noetherian domains.
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...
P*-Invariant ideals in rings of invariants.
Polyèdre caractéristique et éclatements combinatoires.
Polynôme d'Hilbert-Samuel des clôtures intégrales des puissances d'un idéal m-primaire