Continuous rings with ACC on annihilators. (English) Zbl 0767.16004

Camillo, Victor; Yousif, Mohamed F.

Can. Math. Bull. 34, No. 4, 462-464 (1991).

The authors show that a two-sided continuous ring with ascending chain condition on left annihilators is quasi-Frobenius, extending a well-known result of C. Faith from one-sided self-injective rings to two-sided continuous rings. In general, a similar result for one-sided continuous rings is not true.

Reviewer: Dinh van Huynh (Pusan)

MSC:

16L60	Quasi-Frobenius rings
16P60	Chain conditions on annihilators and summands: Goldie-type conditions
16D50	Injective modules, self-injective associative rings
16P20	Artinian rings and modules (associative rings and algebras)

Keywords:

two-sided continuous ring; ascending chain condition; left annihilators; quasi-Frobenius; self-injective rings