# Artinian bimodule with quasi-Frobenius bimodule of translations

## TL;DR

This paper explores the relationship between Artinian bimodules with quasi-Frobenius properties and their translation bimodules, focusing on the structure of associated multiplication and center rings.

## Contribution

It establishes new connections between quasi-Frobenius properties of (A,B)-bimodules and their translation (C,Z)-bimodules over Artinian rings.

## Key findings

- Quasi-Frobenius property transfers under certain conditions.
- Characterization of translation bimodules in the Artinian setting.
- Structural insights into multiplication and center rings.

## Abstract

Let M be an (A,B)-bi-module over left and right respectively Artinian rings. Let C be a multiplication ring of bi-module M, i.e. the ring C is generated by images of a and B in End(M). Let Z be a center of C. Bi-module M over rings C and Z we call a bi-module of translation of (A,B)-bi-module M. We investigate a relationship between the fact that (A,B)-bi-module M is quasi-Frobenius and the fact that (C,Z)-bi-module M is quasi-Frobenius.