On quasi-Frobenius quotient rings of a Gorenstein semi-maximal ring (Q2755273)

The paper deals with Gorenstein orders which are constructed using the Cayley table of Klein's four-group. As the author notes, V. V. Kirichenko proposed to consider this table as the exponent matrix \(K\) of a Gorenstein semi-maximal ring. Let \(A=(K,\mathcal O)\) be such a ring, where \(\mathcal O\) is an arbitrary discrete valuation ring. The main purpose of the paper is to describe all ideals \(I\) (two-sided) of \(A\) such that \(I\) lies in the square of the Jacobson radical \(J(A)\) and the quotient ring \(A/I\) is a quasi-Frobenius ring. The complete list of all ideals consists of 24 types and the immediate verification of the above mentioned conditions gives four types of ideals.