Commutative Rings and Binomial Coefficients.
Commuting polynomial vectors over an integral domain
Composition of binary quadratic forms over integral domains
Conductive Integral Domains as Pullbacks.
Determining Integer-Valued Polynomials From Their Image
This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with Scott T. Chapman, and will appear in [2]. Let represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on .
Differential rings in which any ideal is differential
Dimension de l'anneau des polynomes a valeurs entieres.
Ein Cohen-Macaulay-Kriterium mit Anwendungen auf den Konormalenmodul und den Differentialmodul.
Elasticity of factorizations in atomic monoids and integral domains
For an atomic domain , its elasticity is defined by : for irreducible . We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants defined by : for irreducible . As a main result we characterize all orders in algebraic number fields having finite elasticity. On the way, we obtain a series of results concerning the invariants and for monoids and integral domains which are of independent interest.
Equations for the set of overrings of normal rings and related ring extensions
We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.
Erratum to -primary ideals of a commutative ring
Essential Cover and Closure
2000 Mathematics Subject Classification: 16N80, 16S70, 16D25, 13G05.We construct some new examples showing that Heyman and Roos construction of the essential closure in the class of associative rings can terminate at any finite or the first infinite ordinal.
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.
Finite Polynomial Orbits in Finitely Generated Domains.
Finitely generated projective ideals in commutative rings.
Finiteness theorems for factorizations.
Flat Ideals II.
Fragmented integral domains
-domains and pseudo-valuations
Integral domains of finite character. II.