This article is cited in 1 paper

Bicommutators of fully divisible modules

A. I. Kashu


Abstract: We consider the module $M_R$, injective with respect to the pair $R/K\subseteq E(R/K)$, where $K=0:M$, and form the ring $Q_M (R)$ by constructing rings of quotients with respect to torsion. We find necessary and sufficient conditions on $M_R$ for $Q_M (R)$ to coincide with the bicommutator of $M_R$. Among the consequences of this are the well-known results of Beachy and Morita on bicommutators of coexact fully divisible modules and of injective endofinite modules.
Bibliography: 7 titles.

UDC: 519.48

MSC: Primary 18E40; Secondary 16A08, 16A52

Received: 10.03.1975

 English version: Mathematics of the USSR-Sbornik, 1976, 29:4, 431–440

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