Quasi-Frobenius rings were introduced by Nakayama  in the study of representations of algebras. Afterwards, Quasi-Frobenius rings played a central role in ring theory, and numerous characterizations were given by various authors. In particular, Ikeda characterized these rings as two sided self-injective and two sided Artinian. Numerous investigations have been conducted to improve Ikeda's mentioned result by weakening either the Artinian condition, or the injectivity condition, or both, and this has led to the discovery of new concepts of rings and modules such as simple-injectivity and min-injectivity of rings and modules. Nicholson and Yousif  approached the Ikeda's result with min-injective modules that are more general than injectivity. They show that a right Artinian two sided min-injective ring is quasi-Frobenius. This basic approach is concerned with when a min-injective ring become injective. Considering this point of view, in this talk, we aim to present some new results about the rings whose min-injective right modules are injective.

This is joint work with S. Benli-Goral, E. Buyukasik, J.R. Garcia Rozas and L. Oyonarte.

This study is supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under the 2219 - International Postdoctoral Research Fellowship Program for Turkish Citizens.

There will be a coffee break after the talk.