On Armendariz rings.
On Cohen's theorem
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 coverings of almost Dedekind domains
On domains with ACC on invertible ideals
If is a domain with the ascending chain condition on (integral) invertible ideals, then the group of its invertible ideals is generated by the set of maximal invertible ideals. In this note we study some properties of and we prove that, if is a free group on , then is a locally factorial Krull domain.
On efficient generation of ideals.
On equimultiple ideals.
On Factorization into Prime Ideals
On Finite Conductor Domains.
On finitely generated multiplication ideals in commutative rings
On finitely generated multiplication modules
We shall prove that if is a finitely generated multiplication module and is a finitely generated ideal of , then there exists a distributive lattice such that with Zariski topology is homeomorphic to to Stone topology. Finally we shall give a characterization of finitely generated multiplication -modules such that is a finitely generated ideal of .
On Form Ideals and Artin-Rees Condition.
On generating sets of minimal length for polynomial ideals
On h-regular grades algebras of characteristic p > 0
On Ideal Theory in High Prufer Domains.
On Krull's intersection theorem of fuzzy ideals.
On lifting prime ideals.
On minimal ideals in the ring of real-valued continuous functions on a frame
Let be the ring of real-valued continuous functions on a frame . The aim of this paper is to study the relation between minimality of ideals of and the set of all zero sets in determined by elements of . To do this, the concepts of coz-disjointness, coz-spatiality and coz-density are introduced. In the case of a coz-dense frame , it is proved that the -ring is isomorphic to the -ring of all real continuous functions on the topological space . Finally, a one-one correspondence is...
On mixed multiplicities of homogeneous ideals.
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