Annihilator conditions relative to a class of modules. (English) Zbl 1215.16004
Summary: Annihilator conditions relative to a class of modules are studied and used to characterize the relative extending modules. In particular, dual rings relative to the class of all small right ideals, called right small-dual rings, are investigated and some known results on the dual rings are generalized to the case of small-dual rings.
MSC:
| 16D50 | Injective modules, self-injective associative rings |
| 16D70 | Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) |
| 16D80 | Other classes of modules and ideals in associative algebras |
| 16P70 | Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) |
