Face numbers and nongeneric initial ideals.
Face vectors of two-dimensional Buchsbaum complexes.
Factorial extensions of regular local rings and invariants of finite groups.
Factorial Fermat curves over the rational numbers
A polynomial f in the set {Xⁿ+Yⁿ, Xⁿ +Yⁿ-Zⁿ, Xⁿ +Yⁿ+Zⁿ, Xⁿ +Yⁿ-1} lends itself to an elementary proof of the following theorem: if the coordinate ring over ℚ of f is factorial, then n is one or two. We give a list of problems suggested by this result.
Factorialite de l΄algebre affine de certaines formes quadratiques
Factoriality of a ring of holomorphic functions
Factorisation de Ritt pour les polynômes exponentiels formels
Factorisation de suites récurrentes linéaires
Factorisation de suites récurrentes linéaires et applications
Factorisations de morphismes d'anneaux commutatifs
Factorization in Krull monoids with infinite class group
Let H be a Krull monoid with infinite class group and such that each divisor class of H contains a prime divisor. We show that for each finite set L of integers ≥2 there exists some h ∈ H such that the following are equivalent: (i) h has a representation for some irreducible elements , (ii) k ∈ L.
Factorization properties of Krull monoids with infinite class group
For a non-unit a of an atomic monoid H we call the set of lengths of a. Let H be a Krull monoid with infinite divisor class group such that each divisor class is the sum of a bounded number of prime divisor classes of H. We investigate factorization properties of H and show that H has sets of lengths containing large gaps. Finally we apply this result to finitely generated algebras over perfect fields with infinite divisor class group.
Failure of splitting from module-finite extension rings.
Faithfully quadratic rings - a summary of results
This is a summary of some of the main results in the monograph Faithfully Ordered Rings (Mem. Amer. Math. Soc. 2015), presented by the first author at the ALANT conference, Będlewo, Poland, June 8-13, 2014. The notions involved and the results are stated in detail, the techniques employed briefly outlined, but proofs are omitted. We focus on those aspects of the cited monograph concerning (diagonal) quadratic forms over preordered rings.
Families of almost finite character
Families of functions dominated by distributions of -classes of mappings
A subsheaf of the sheaf of germs functions over an open subset of is called a sheaf of sub function. Comparing with the investigations of sheaves of ideals of , we study the finite presentability of certain sheaves of sub -rings. Especially we treat the sheaf defined by the distribution of Mather’s -classes of a mapping.
Families of reduced zero-dimensional schemes.
A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hilbert sheme is reducible. Furthermore, we show that the Weak Lefschetz Property holds for the general element...
Fast invertierbare Primideale der kommutativen Ringe.
Fermeture intégrale et changement de base
Fermeture intégrale et changement de base