Nouvelles caracterisations des v-anneaux et des anneaux pseudo-frobeniusiens¹

On commutative rings whose maximal ideals are idempotent

“…their classes of modules which are socle-fine (radical-fine). In this way D. M. Baquero, A. Idelhadj, C. M. González, A. Kaidi and A. Yahya have proved important results that can be found in [11], [12], [13], [14] and [15]. Nevertheless, most of the classes considered have homological properties (as projectivity and injectivity) and the problem of characterizing rings over which a class of modules satisfying a chain condition (as the ascending or the descending chain condition or having a composition series) is socle-fine (radical-fine) seems to be never considered before.…”

Rings whose class of projective modules is socle fine

“…Continuing this philosophy, artinian and noetherian rings are characterized in [16] by socle fine classes. The interesting paper [12] contains also characterizations for V -rings and pseudo-Frobenius rings. Complementary literature on socle and radical fine classes can be found in [13], [17] and [10].…”