Modüllerin Baer-Kaplansky Sınıfları Üzerine Bir Çalışma

Abstract

If A and B are torsion groups whose EndZ(A) and EndZ(B) are isomorphic with Ψ, then A and B are isomorphic. Moreover, if A and B are isomorphic with ϕ, then Ψ(η) = ϕηϕ−1. This expression is known as “Baer-Kaplansky Theorem”. This thesis consists of five chapters. In the first chapter, the subject of the thesis is introduced and some studies are mentioned. The second chapter contains the preliminary information necessary for the study. In the third chapter, the Baer-Kaplansky Theorem is elaborated and examples are given. In the fourth chapter, with the help of IP-isomorphism, classes of modules satisfying the Baer-Kaplansky property are studied. The last part of the thesis is the original part. In this part, a ring R is constructed. It is shown that for this ring the category Mod-R does not satisfy the Baer-Kaplansky property. Also, the Baer-Kaplansky property of some module classes are analysed.