A class of principal ideal rings arising from the converse of the Chinese remainder theorem.
A natural map from the ext Künneth sequence to the Tor one.
A simple proof of uniqueness for torsion modules over principal ideal domains.
The aim of this note is to give an alternative proof of uniqueness for the decomposition of a finitely generated torsion module over a P.I.D. (= principal ideal domain) as a direct sum of indecomposable submodules.Our proof tries to mimic as far as we can the standard procedures used when dealing with vector spaces.For the sake of completeness we also include a proof of the existence theorem.
A theory of multiplicity for multiplictive filtrations.
An example of a Fréchet algebra which is a principal ideal domain
We construct an example of a Fréchet m-convex algebra which is a principal ideal domain, and has the unit disk as the maximal ideal space.
Anneaux locaux et unisériels
Artin's conjecture on primes with prescribed primitive roots
Commutative semigroup rings which are principal ideal rings
Euclidean function fields.
Euclidean Number Fields of Large Degree
Isomorphic cohomology Yields isomorphic homology.
On Artin's Conjecture and Euclid's Algorithm in Global Fields.
On commutative FGI-Rings.
On commutative principal ideal semigroup rings.
On commutative rings whose prime ideals are direct sums of cyclics
In this paper we study commutative rings whose prime ideals are direct sums of cyclic modules. In the case is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that for a local ring , the following statements are equivalent: (1) Every prime ideal of is a direct sum of cyclic -modules; (2) where is an index set and is a principal ideal ring for each ; (3) Every prime ideal of is a direct sum of at most...
On finite principal ideal rings.
On prime submodules and primary decomposition
We characterize prime submodules of for a principal ideal domain and investigate the primary decomposition of any submodule into primary submodules of
On symplectic groups over polynomial rings.
On the diagonals of integral matrices
Principal ideal theorems for holomorphy rings in fields.