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
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.
Families of almost finite character
Fast invertierbare Primideale der kommutativen Ringe.
Fields of Large Transcendence Degree Generated by Values of Elliptic Functions.
Filtrations by complete ideals and applications.
Finding a cluster-tilting object for a representation finite cluster-tilted algebra
We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.
Finite automata and algebraic extensions of function fields
We give an automata-theoretic description of the algebraic closure of the rational function field over a finite field , generalizing a result of Christol. The description occurs within the Hahn-Mal’cev-Neumann field of “generalized power series” over . In passing, we obtain a characterization of well-ordered sets of rational numbers whose base expansions are generated by a finite automaton, and exhibit some techniques for computing in the algebraic closure; these include an adaptation to positive...
Finite bases for integral closures.
Finite cyclic groups and the k-HFD property
Finite mutation classes of coloured quivers
We show that the mutation class of a coloured quiver arising from an m-cluster tilting object associated with a finite-dimensional hereditary algebra H, is finite if and only if H is of finite or tame representation type, or it has at most two simples. This generalizes a result known for cluster categories.