Page 1 PURE AND APPLIED MATHEMATICS ASeries of Monographs and Textbooks LINEAR
ALGEBRA OVER COMMUTATIVE RINGS Bernard R. McDonald Page 2 Linear Algebra Over …

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 …

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

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 …

This survey covers material in Referativnyi Zhurnal Matematika and is a continuation of AV
Mikhalev's survey in Algebra. Topology. Geometry, Vol. 12 (Itogi Nauki i Tekhniki (1974)) …

We identify a large class of rings over which locally free modules are determined by their
endomorphism rings. We characterize these endomorphism rings and consider under what …

In view of Lemma 2.2 we ma, and do, regard endomorphisms of C as endomorphisms of B.
Let E= ER (B) and set 1 (B)={4 a EB4 B}. It is clear that 1 (B) is a left ideal of 8. 1 (B) will play …

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 …

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 …