AMS Graduate Chapter Seminar, Jan. 24

The AMS Graduate Chapter at Ohio University has scheduled an in-person seminar for Wednesday, Jan. 24, 2024, from 4:10 to 5:05 p.m. in Morton Hall 219. We are delighted to announce that our guest speaker for the talk will be Dr. Fatma Ebrahim, an assistant professor at the Faculty of Science, AL-Azhar University, Egypt. Dr. Ebrahim is also a visiting scholar hosted by the Ohio University Center of Ring Theory and its Applications.

Title : On Schröder-Bernstein property for Modules

Abstract : The well-known Schröder -Bernstein Theorem states that any two sets with one-to-one maps into each other are isomorphic. The question of whether any two (subisomorphic or) direct summand subisomorphic algebraic structures are isomorphic, has long been of interest. Kaplansky asked whether direct summands subisomorphic abelian groups are always isomorphic. The question generated a great deal of interest. The study of this question for the general class of modules has been somewhat limited. In This talk, we extend the study of this question for modules. We say that a module $M$ {\it satisfies the Schröder-Bernstein property (S-B property)} if any two direct summands of $M$ which are subisomorphic to direct summands of each other, are isomorphic. We show that a large number of classes of modules satisfy the S-B property. These include the classes of quasi-continuous, directly finite, quasi-discrete, and modules with ACC on direct summands.