On small-dual rings. (Chinese. English summary) Zbl 1212.16015
Summary: This paper mainly investigates the rings such that small left ideals are left annihilators, namely, left small-dual rings, and gives some conditions to assure the nilpotency of \(J(R)\), and also obtains some properties of small-dual semilocal rings.
MSC:
| 16D80 | Other classes of modules and ideals in associative algebras |
| 16D50 | Injective modules, self-injective associative rings |
| 16P60 | Chain conditions on annihilators and summands: Goldie-type conditions |
| 16L30 | Noncommutative local and semilocal rings, perfect rings |
