NOETHER (ARTIN) CLASSICAL QUOTIENT RINGS OF DUO RINGS AND PROJECTIVITY AND INJECTIVITY OF SIMPLE MODULES OVER DUO RINGS

We call a fight injective module E_R Σ(△)-injective if the right annihilators of E_R in R satisfy ascending (descending)chain condition. And a ring R with identity is called a Duo ring if every one-sided ideal is a two-sided ideal. A ring is called a right Σ(△)ring if