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On non singular p-inyective rings.

Yasuyuki Hirano (1994)

Publicacions Matemàtiques

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 presentations of semigroup rings

Mario Petrich, Pedro V. Silva (1999)

Bollettino dell'Unione Matematica Italiana

Siano I un ideale di un anello R e σ una congruenza su un semigruppo S . Consideriamo l'anello semigruppo R / I ⁢ S / σ come un'immagine omomorfa dell'anello semigruppo R ⁢ S . Questo è fatto in tre passi: prima studiando l'anello semigruppo R ⁢ S / σ , poi R / I ⁢ S 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 C -algebre, dove C è un anello commutativo, possono essere facilmente dedotti. Alcuni raffinamenti, casi speciali...

On p-semirings

Branka Budimirović, Vjekoslav Budimirović, Branimir Šešelja (2002)

Discussiones Mathematicae - General Algebra and Applications

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

Horea Florian Abrudan (2011)

Czechoslovak Mathematical Journal

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 A for which End c ( A ) is regular is given.

On rings all of whose modules are retractable

Şule Ecevit, Muhammet Tamer Koşan (2009)

Archivum Mathematicum

Let R be a ring. A right R -module M is said to be retractable if 𝕋 H o m R ( M , N ) ≠ 0 whenever N is a non-zero submodule of M . The goal of this article is to investigate a ring R for which every right R-module is retractable. Such a ring will be called right mod-retractable. We proved that ( 1 ) The ring ∏ i ∈ ℐ R i is right mod-retractable if and only if each R i is a right mod-retractable ring for each i ∈ ℐ , where ℐ is an arbitrary finite set. ( 2 ) If R [ x ] is a mod-retractable ring then R is a mod-retractable ring.

On semifir monoid rings.

Ferrán Cedó Gine (1989)

Publicacions Matemàtiques

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.

Currently displaying 61 – 80 of 139