… Let RN be a left R-module and let B = End RM be its endomorphism ring. When … , Gl and
G2, which exist between the lattice, L, of submodules of M and the lattices, L, or L,, of right or left …

… serial modules and their endomorphism rings. In particular, theAlbu-Nastasescu conjecture
is shown to be valid for faithful serial modules … lattice satisfies both distributive laws. These …

… by elements of its lattice … show that the endomorphism ring of a module which is the direct
sum of more than three isomorphic submodules is determined up to isomorphism by its lattice …

… -module, it is always possible to find a A-lattice X such that KX-= X as KA-modules; such a
A-lattice X … If X is contained in X, Curtis and Reiner call it a full A-lattice in X.) From now on we …

… modules whose endomorphism rings have commuting idempotents, or in which one-sided
ideals are two-sided. We also consider modules … H and I are complete lattices under inclusion. …

… consists in proving that the module V is a self… module V need not be a self-generator;
however, we show, in Section 2, that an “approximation” of self-generation is sufficient for the lattice …

… modules RM, not necessarily unital or faithful, over rings R not necessarily containing a 1. We
denote the lattice … that E is a lattice isomorphism between the lattices of submodules of RM …

… / = JC\R* and I>—>I = RI are reciprocal lattice isomorphisms … we prove that the endomorphism
ring of an ideal of R is regular, … If A is any 5-module with homological dimension at least 2, …

… V, or QI, ring to simple rings. The latter are characterized as those right Noetherian rings
for which the endomorphism ring of any indecomposable injective right module is a field (see …

… modules. It is however a comparative triviality to give an example of such a module
whose endomorphism ring is not an order in the endomorphism ring of its injective hull M. …