A characterization of Krull rings with zero divisors
It is proved that a Marot ring is a Krull ring if and only if its monoid of regular elements is a Krull monoid.
A characterization of Prüfer rings.
A class of multiplicative lattices
We study the multiplicative lattices which satisfy the condition for all . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group or . A sharp lattice localized at its maximal elements are totally ordered sharp lattices. The converse is true if has finite character.
A class of torsion-free abelian groups characterized by the ranks of their socles
Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups, bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket -module is tensor a bracket group.
A criterion for rings which are locally valuation rings
Using the notion of cyclically pure injective modules, a characterization of rings which are locally valuation rings is established. As applications, new characterizations of Prüfer domains and pure semisimple rings are provided. Namely, we show that a domain R is Prüfer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semisimple if and only if every R-module is cyclically pure...
A General Theory of Almost Factoriality.
A local characterization of Prüfer rings.
A note on the dual of a finitely generated multiplication module
A strong complement property of Dedekind domains
A structure theorem for sets of lengths
A theory of multiplicity for multiplictive filtrations.
A “-operation free” approach to Prüfer -multiplication domains.
A weakening of the euclidean property for integral domains and applications to algebraic number theory. II.
A weakening of the euclidean property for integral domains and applications to algebraic number theory. I.
Abelian Groups with an Endomorphism with Irreducible minimum Polynomial
Almost Artinian modules.
Almost Diagonal Matrices over Dedekind Domains.
Almost triangular matrices over Dedekind domains.
Arithmetic of block monoids
Arithmetical properties of finite rings and algebras, and analytic number theory. III. Finite modules and algebras over Dedekind domains.