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 …

References Page 1 References [1] FW Anderson and KR Fuller, Rings and Categories of
Modules, SpringerVerlag, New York (1974). [2] VI Arnautov, ST Glavatsky, and AV Mikhalev …

Let A and B be rings and Mand Në a right A-module and a right B-module respectively. Let
a: End (MA)→ End (NB) be either an isomorphism or an anti-isomorphism of their …

Discrete valuation domains form a class of local domains close to division rings. However, it
follows from our definition that a division ring is not a discrete valuation domain. A discrete …

Аннотация В обзорной статье представлен анализ результатов теории абелевых
групп, а также колец и модулей, которые касаются определяемости алгебраических …

This book provides the first systematic treatment of modules over discrete valuation
domains, which play an important role in various areas of algebra, especially in commutative …

This review paper is a continuation of two previous review papers devoted to properties of
modules over discrete valuation domains. The first part of this work was published in the …

We will prove that if G and H are modules over a principal ideal domain R such that the
endomorphism rings \End_R(R⊕G) and \End_R(R⊕H) are isomorphic, then G≅H …

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We derive a necessary and sufficient condition that an isomorphism between the
endomorphism rings of modules be induced by a semi-linear isomorphism of the modules …