Speaker: Christian Lomp (Universidade Do Porto, Portugal)
Title: On dual Kasch rings
Abstract: Seven decades ago, Friedrich Kasch, in his work on Frobenius extensions, considered rings that satisfy the condition that every proper left ideal has a nonzero right annihilator, and every proper right ideal has a nonzero left annihilator. In his honor, rings in which every proper right ideal has a nonzero left annihilator are termed right Kasch rings. Right Kasch rings are intimately linked to Frobenius extensions, Frobenius algebras, and more generally, to quasi-Frobenius rings. Many equivalent conditions for a ring R to be a right Kasch ring are known. For example, R is right Kasch if and only if its injective hull is an injective cogenerator if and only if any simple right R-module embeds into R. In this talk, I will address the recently introduced dual notion of Kasch rings and demonstrate how it relates to Kasch rings. This work is joint work with Engin Büyükasık and Haydar Baran Yurtsever.
