EuDML | Browse

In this paper, we introduce a subclass of strongly clean rings. Let $R$ be a ring with identity, $J$ be the Jacobson radical of $R$ , and let $J^{#}$ denote the set of all elements of $R$ which are nilpotent in $R / J$ . An element $a \in R$ is called very $J^{#}$ -clean provided that there exists an idempotent $e \in R$ such that $a e = e a$ and $a - e$ or $a + e$ is an element of $J^{#}$ . A ring $R$ is said to be very $J^{#}$ -clean in case every element in $R$ is very $J^{#}$ -clean. We prove that every very $J^{#}$ -clean ring is strongly $π$ -rad clean and has stable range one. It is shown...

A theorem on direct products of Slender modules

John D. O'Neill (1987)

Rendiconti del Seminario Matematico della Università di Padova

A weaker form of Baer’s splitting problem for torsion theories

Mark L. Teply, Blas Torrecillas (1993)

Czechoslovak Mathematical Journal

Algebraically compact modules

Alberto Facchini (1985)

Acta Universitatis Carolinae. Mathematica et Physica

Almost Abelian rings

Junchao Wei (2013)

Communications in Mathematics

A ring $R$ is defined to be left almost Abelian if $a e = 0$ implies $a R e = 0$ for $a \in N (R)$ and $e \in E (R)$ , where $E (R)$ and $N (R)$ stand respectively for the set of idempotents and the set of nilpotents of $R$ . Some characterizations and properties of such rings are included. It follows that if $R$ is a left almost Abelian ring, then $R$ is $π$ -regular if and only if $N (R)$ is an ideal of $R$ and $R / N (R)$ is regular. Moreover it is proved that (1) $R$ is an Abelian ring if and only if $R$ is a left almost Abelian left idempotent reflexive ring. (2) $R$ is strongly...

Anneaux semi-artiniens

Constantin Năstăsescu, Nicolae Popescu (1968)

Bulletin de la Société Mathématique de France

Associative rings and the Whitehead property of modules [Abstract of thesis]

Jan Trlifaj (1990)

Commentationes Mathematicae Universitatis Carolinae

Displaying 1 – 12 of 12

Currently displaying 1 – 12 of 12