Influence of the Baer–Kaplansky Theorem on the Development of the Theory of Groups, Rings, and Modules
EA Blagoveshchenskaya, AV Mikhalev - Journal of Mathematical Sciences, 2023 - Springer
The review presents an analysis of results of the Abelian group theory, as well as rings and
modules, which concern the definability of algebraic structures by their endomorphism rings …
modules, which concern the definability of algebraic structures by their endomorphism rings …
Baer-Kaplansky classes of vector spaces and modules determined by numerical invariants
G D'Este, DK Tütüncü, R Tribak - Communications in Algebra, 2023 - Taylor & Francis
We show that reasonably large classes C of vector spaces, modules over noncommutative
algebras and abelian groups are Baer-Kaplansky classes with additional properties. Indeed …
algebras and abelian groups are Baer-Kaplansky classes with additional properties. Indeed …
Влияние теоремы Бэра—Капланского на развитие теории групп, колец и модулей
ЕА Благовещенская, АВ Михалёв - Фундаментальная и прикладная …, 2022 - mathnet.ru
Аннотация В обзорной статье представлен анализ результатов теории абелевых
групп, а также колец и модулей, которые касаются определяемости алгебраических …
групп, а также колец и модулей, которые касаются определяемости алгебраических …
A Baer-Kaplansky Theorem in additive categories
S Crivei, D Keskin Tütüncü, R Tribak - Ring Theory 2019 …, 2021 - World Scientific
We prove the following Baer-Kaplansky Theorem in additive categories. If M and N are
objects of an additive category C such that:(1) M= A⨁ X and N= B⨁ X for some objects A, B …
objects of an additive category C such that:(1) M= A⨁ X and N= B⨁ X for some objects A, B …