On module categories with nilpotent infinite radical
On *-modules generating the injectives
On modules with Le-decomposition.
On non singular p-inyective rings.
A ring R is said to be left p-injective if, for any principal left ideal I of R, any left R-homomorphism I into R extends to one of R into itself. In this note left nonsingular left p-injective rings are characterized using their maximal left rings of quotients and the structure of semiprime left p-injective rings of bounded index is investigated.
On p.p.-rings which are reduced.
On presentations of semigroup rings
Siano un ideale di un anello e una congruenza su un semigruppo . Consideriamo l'anello semigruppo come un'immagine omomorfa dell'anello semigruppo . Questo è fatto in tre passi: prima studiando l'anello semigruppo , poi e infine combinando i due casi speciali. In ciascun caso, determiniamo l'ideale che è il nucleo dell'omomorfismo in questione. I risultati corrispondenti per le -algebre, dove è un anello commutativo, possono essere facilmente dedotti. Alcuni raffinamenti, casi speciali...
On products of singular elements
On p-semirings
A class of semirings, so called p-semirings, characterized by a natural number p is introduced and basic properties are investigated. It is proved that every p-semiring is a union of skew rings. It is proved that for some p-semirings with non-commutative operations, this union contains rings which are commutative and possess an identity.
On regular endomorphism rings of topological Abelian groups
We extend a result of Rangaswamy about regularity of endomorphism rings of Abelian groups to arbitrary topological Abelian groups. Regularity of discrete quasi-injective modules over compact rings modulo radical is proved. A characterization of torsion LCA groups for which is regular is given.
On rings all of whose modules are retractable
Let be a ring. A right -module is said to be retractable if whenever is a non-zero submodule of . The goal of this article is to investigate a ring for which every right R-module is retractable. Such a ring will be called right mod-retractable. We proved that The ring is right mod-retractable if and only if each is a right mod-retractable ring for each , where is an arbitrary finite set. If is a mod-retractable ring then is a mod-retractable ring.
On rings satisfying certain polynomial identities.
On rings whose centers are Galois extensions
On rings whose flat modules form a Grothendieck category
On rings with zero divisors. Strong -groups
On rings with zero total.
On semifir monoid rings.
We give a new condition on a monoid M for the monoid ring F[M] to be a 2-fir. Furthermore, we construct a monoid M that satisfies all the currently known necessary conditions for F[M] to be a semifir and that the group of units of M is trivial, but M is not a directed union of free monoids.
On semigroup rings.
On separable Abelian extensions of rings.
On separable extensions of group rings and quaternion rings.
On Separable Subalgebras of Azumaya Algebras