arXiv subjects

Truong Cong Quynh

Publications and source records attributed to Truong Cong Quynh.

6 recordsLinked to original sources

arXiv2026

Hereditarily and Super Bassian Modules over Certain Rings

We characterize in certain basic cases when a module over a ring is either {\it hereditarily Bassian} or {\it super Bassian} in the sense that either each its proper submodule is Bassian or, respectively, each its proper epimorphic image is Bassian. We prove several structural criteria for both hereditarily Bassian and super Bassian modules over non-primitive Dedekind prime rings, and in particular Dedekind domains. Over these rings, we establish that a singular module is super Bassian exactly when it is Bassian, which is true if and only if it is Bassian. In addition, for an arbitrary (not necessarily singular) module over a non-primitive Dedekind prime ring, the property of being super Bassian curiously implies the property of being hereditary Bassian always. Our results somewhat continue and supply recent results due to Tuganbaev in Mathematics (2026) and Blacher in J. Algebra (2026).

math.RA↗

arXiv2022

Rings whose ideals are close to automorphism-invariant

We consider rings whose one-sided ideals are close to automorphism-invariant modules. We study rings in which every (finitely generated) right ideal is automorphism invariant and rings in which every right ideal is a finite direct sum of automorphism invariant ideals. Connections between these classes of rings, $q$-ring and $Σ$-$q$-rings are also considered

math.RA↗

arXiv2017

Periodic and q-potent elements in rings

This paper, we consider some properties of rings via q-potent and periodic elements. In this paper we give some results of rings in which every element is a sum of an idempotent and a q-potent that commute; periodic rings and k-potent elements of algebras.

math.RA↗

arXiv2016

Modules close to SSP- and SIP-modules

In this paper, we investigate some properties of SIP, SSP and CS-Rickart modules. We give equivalent conditions for SIP and SSP modules; establish connections between the class of semisimple artinian rings and the class of SIP rings. It shows that $R$ is a semisimple artinian ring if and only if $R_R$ is SIP and every right $R$-module has a SIP-cover. We also prove that $R$ is a semiregular ring and $J(R) = Z(R_R)$ if only if every finitely generated projective module is a SIP-CS module which is also a $C2$ module.

math.RA↗

arXiv2016

On classes of C3 and D3 modules

The aim of this paper is to study the notions of $\mathcal{A}$-C3 and $\mathcal{A}$-D3 modules for some class $\mathcal{A}$ of right modules. Several characterizations of these modules are provided and used to describe some well-known classes of rings and modules. For example, a regular right $R$-module $F$ is a $V$-module if and only if every $F$-cyclic module $M$ is an $\mathcal{A}$-C3 module where $\mathcal{A}$ is the class of all simple submodules of $M$. Moreover, let $R$ be a right artinian ring and $\mathcal{A}$, a class of right $R$-modules with local endomorphisms, containing all simple right $R$-modules and closed under isomorphisms. If all right $R$-modules are $\mathcal{A}$-injective, then $R$ is a serial artinian ring with $J^{2}(R)=0$ if and only if every $\mathcal{A}$-C3 right $R$-module is quasi-injective, if and only if every $\mathcal{A}$-C3 right $R$-module is C3.

math.RA↗

arXiv2015

Rings with each right ideal automorphism-invariant

In this paper, we study rings having the property that every right ideal is automorphism-invariant. Such rings are called right $a$-rings. It is shown that (1) a right $a$-ring is a direct sum of a square-full semisimple artinian ring and a right square-free ring, (2) a ring $R$ is semisimple artinian if and only if the matrix ring $\mathbb{M}_n(R)$ for some $n>1$ is a right $a$-ring, (3) every right $a$-ring is stably-finite, (4) a right $a$-ring is von Neumann regular if and only if it is semiprime, and (5) a prime right $a$-ring is simple artinian. We also describe the structure of an indecomposable right artinian right non-singular right $a$-ring as a triangular matrix ring of certain block matrices.

math.RA↗