A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

The aim of this paper is to review thoroughly the applications ∩ -large pseudo N-injective acts in quasi-Frobenius monoid theory, and therefore, relationship with some class injectivity studied. Applications properties injective theory are proven. Also, it’s proved that subsequent parity, every union (direct sum) two a act if only under Noetherian condition for right S. Additionally, we categor...

Résumé. On sait que les complétions profinies d’un semigroupe libre qui sont associées à une pseudovariété de semigroupes ou de semigroupes ordonnés peuvent être définies par un écart ou un quasi-écart. Nous caractérisons les quasi-écarts et les quasi-uniformités qui peuvent être obtenues de cette façon. Nous démontrons également l’existence d’une correspondance injective “à la Eilenberg”, entr...

We show that every quasi–norm p on a (real) cancellative cone X induces in a natural way an extended quasi–metric ep on X for which (X, ep) is an extended quasi–metric cone. We prove that the structure of a quasi– normed cone is preserved by bicompletion, under bijective isometries. In fact, we observe that isometries are not necessarily injective in this setting. Some illustrative examples are...