Elasticity in certain block monoids via the Euclidean table
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
Etale covers, bimodules and differential operators.
Euclidean quadratic forms and ADC forms II: integral forms
We study ADC quadratic forms and Euclidean quadratic forms over the integers, obtaining complete classification results in the positive case.
Every Cotorsion-free Algebra is an Endomorphism Algebra.
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.
Families of almost finite character
Fast invertierbare Primideale der kommutativen Ringe.
Finite bases for integral closures.
Finite cyclic groups and the k-HFD property
Fractions rationnelles à valeurs entières
Fragmented integral domains
Functorial Subgroups Commuting with Inverse Limits.
Galois modules and embedding problems.
Gaussian and Prüfer conditions in bi-amalgamated algebras
Let and be two ring homomorphisms and let and be ideals of and , respectively, such that . In this paper, we investigate the transfer of the notions of Gaussian and Prüfer rings to the bi-amalgamation of with along with respect to (denoted by introduced and studied by S. Kabbaj, K. Louartiti and M. Tamekkante in 2013. Our results recover well known results on amalgamations in C. A. Finocchiaro (2014) and generate new original examples of rings possessing these properties.
Generalized equivalence of matrices over Prüfer domains.
Generalized GCD rings.
Generalized GCD rings II.